Soli Deo Gloria!
I must say, as one unfamiliar with this war, that Britain was financially weaker than I expected, perhaps representing their limited commitment to a continental war. Their base income is 6. They can expect to be without Münster for most of the game, and they might not have Hanover in spring 1758, if the French are able to play Kloster-Zeven. However, they will likely collect for colonial conflict in 1759 and later, though that's highly dependent on when Typhus strikes. Also, they might take Frankfurt am Main or some other Imperial fortresses at some point. We'll estimate their total springtime income as about 28 thaler. Sustainment costs 6/turn, leaving them around 2 short over the game. Devastation isn't really an issue, considering that Westphalia is fairly robust (24 FPs) and in the least vicious KK theater.
Credit: 6/-1 MW or 11/-2 MW until Spain enters.
Cards: Britain's Outrage (2), Reinforcing Continental Success (4), War with Spain (3), Manila and Havana (6).
War with Spain is not certain to be played, as France might get Family Compact and play it first. So we'll figure on 12 thaler from cards.
Other deductions: Prussian subsidy, 7 thaler. The Prussians will probably want two years of subsidy (see below), for a total of 14 thaler, although you might not feel the same way. Given your 8 starting thaler, this leaves you with about 4 thaler before credit and recruiting.
A-A recruiting will average 3 thaler/year, assuming you don't pay the extra 3 for a positive DRM. So hit that credit hard! You can afford to spend MW there, since: you won't lose any to enemy cards; you're not likely to lose any to colonial conflict; you won't lose more than one to devastation; you shouldn't suffer any crushing defeats; and you ought to be able to hold Hanover from 1758 on if you're careful. Plus, your credit ends when Spain enters the picture, so get what you can while the gettin's good!
Prussia has a tenuous economic position. Their base income is only 7 thaler, of which they can expect to lose 2 (Konigsberg and Minden) in 1757. However, assuming historical diplomacy, they will gain 5 thaler from Saxony, which they can expect to hold through most of the game, plus a further 1 from Lubeck. Konigratz is also a possibility, as are Prag, Olmutz, and Brunn, but we'll ignore those. This gives a rough figure of 11 thaler/year, minus devastation. Now, of course, this doesn't cover their yearly sustainment cost of 14. Over the course of an average game, they'll probably be short about 25 thaler for sustainment. This is OK considering that they have a few other sources of income.
A) They can get a 7 thaler subsidy from Britain. This will end sooner than you'd like, but while it lasts it's quite handy. In a historical game this is likely to start in 1758 or 1759 and probably end around the time Spain becomes belligerent. Two years of subsidy is probably the most you can expect, for 14 thaler total.
B) They have three one-shot thaler cards: Saxony Despoiled and Saxony Ravaged are each worth up to 15 thaler, while Extorted Loans just gives D6+1; this yields a total of, say, 34 thaler.
C) They can Devalue the Thaler. This yields 10 thaler (and subtracts 2 from enemy powers) for a cost of 1 or 2 MW. Ideally, you'll want to do this only every other year, to keep your MW stronger. So over a six-spring game, you'll get 30 thaler from devaluation.
Total "other" income: 78.
Of course, there are also some "other" deductions: 1 for East Prussian Policy Change and 2 for each iteration of Blockade of Stettin and Polish Grain Embargo.
Total "other” deductions: say 9 thaler.
Grand total discretionary cash: 78-9=69; 69-25=44; 44+their starting 12=56. This might just cover their recruiting, figuring three years of full recruiting at 11 thaler/year and three years of exhausted recruiting at 6 thaler/year. If they rebuild one step of artillery per year, that gives a total of 57 thaler for recruiting. If necessary, the Prussians can always cash in 2 MW for an extra devaluation and get 10 thaler more. So if the war isn't going too poorly, the Prussians may be able to stay out of the red.
France is the Arsenel of Absolutism! Or something like that. Their base income is 9. They can count on holding Münster pretty much the whole game, Minden for at least one year, and they might manage a few more thaler from assorted A-A spaces. Let's figure a total income of 53 from 1758-1762. Sustainment costs 11/turn, leaving just a slight shortfall. Like Britain, they don't have to worry much about devastation.
Credit: 13/-1 MW or 23/-2 MW until Quebec falls (generally 1759). Take all you can, usually 46.
Colonial conflict is unlikely to give any French income.
Cards: Monmartel & Laborde (only after Quebec) is variable. If you get one play of it when the British don't enjoy Heavy Advantage and two when they do, that might yield around 30 thaler.
Negative cards: Swedish Allies (2 thaler), Danish Subsidy (1 thaler each time you play it), French Fleet (6 thaler to mount an invasion threat), Fall of Quebec (6 thaler). Assuming you don't try the invasion threat, we'll figure 10 thaler lost here.
Recruiting: Somewhere around 11/year until exhaustion, 6 thereafter. Let's say 45 thaler total.
This, plus their starting 7, leaves around 30 thaler for subsidies.
Subsidy: With historical diplomacy, you'll pay 9 from 1758 until you reduce to 3rd Versailles, which costs only 1. This means you can probably provide the 2nd Versailles subsidy twice and 3rd three times, for a total of 21 thaler. You might manage three years of 2nd Versailles, in which case the Austrians should be kissing your feet.
Now there are a lot of variables in here. Recruiting is always an unknown, as is Monmartel & Laborde. You don't know how much you'll get from Hanoverian territory. I'd say, though, to keep the subsidy going as long as you can, even at the expense of some recruiting, but DON'T go in the red! If you do, you'll lose M & L and probably end up in the red even more.
Much more straightforward than France. They get a base 8, +1 for Konigsberg, which exactly covers their sustainment. They have no areas on the map, so devastation is not an issue.
Card income: East Prussian Policy Change (2 thaler).
Subsidy: 2/turn from 2nd Versailles; probably twice; total 4 thaler.
Other deductions: Thaler devaluation; figure on three times per game, so -3 thaler.
Credit: 7/-1 MW available forever. Their credit never ends until Elizabeth dies.
You're recruiting mostly on credit, but since your base recruiting cost averages only 3/year, that's fine. If you've taken heavy losses, you might pay the extra 3 to get a +4 DRM, then probably pay another 3 above your usual cost. Anyway, there's not much to say here; take credit when you need it and if you don't, then don't.
This is another hair-raising one. Their base income is the highest at 11/turn, matching their sustainment, but devastation takes a heavy toll on them. Plus, they'll probably have to cover Imperial shortfalls from time to time.
Base income: 11/turn; game-total 66 thaler.
Sustainment: 11/turn, 8/turn after reduced forces. We'll say the total is 60 thaler.
Credit: 7/-1 MW until Halley's Comet (almost certainly 1758), so you can expect 14 thaler here.
Subsidy: 1st Versailles (2), 2nd Versailles (6), 3rd Versailles (1). You'll get 1st once, 2nd probably twice, and 3rd probably 4 times. Total: 18 thaler.
Card income: Karl von Zinzendorf (3D6+2; D6+2 after exhaustion). I'm mostly guessing here, but I'll say you can play this one twice before exhaustion and three times after, yielding maybe 42 thaler. (In my limited experience Austria usually gets exhausted pretty quickly, what with crushing defeats, key cities, and devastation.) Limited Credit doesn't get you much. Average is 5.5 before exhaustion (but since it's a WW card, you might not get the chance), 1.5 afterward. I'll pick a number out of the air and say it's worth 8 thaler over the course of the game, mostly because that gives me a nice neat 50 for card income.
Devastation: If Bohemia and Moravia are devastated by spring 1759, Saxony and Mecklenburg by '60, Austria, Bavaria and the Rhineland by '61, that means you're losing a total of 20 thaler during the game. (Note: I'm assuming that you're covering Imperial shortfalls due to devastation).
Other deductions: Imperial Auxiliaries (1 thaler). You'll probably play this at least twice. Thaler devaluation will likely cost you 3.
Recruitment: average of 11/turn before exhaustion, 6/turn afterward, plus at least 1 for artillery maintenance. If you reduce the force, you'll recruit only 5 times during the game – say three times before exhaustion and twice times after; total of 51 thaler.
All of this taken together leaves Austria in the black by 12 thaler, which is wonderful. Notice, though, that we assumed you wouldn't lose any thaler spaces other than Saxony, would reduce the force early, and would play Zinzendorf and Limited Credit at every opportunity. The first of those is unlikely in my opinion; the second makes the first even more unlikely, and the third, while doable, gives you less flexibility to respond to Prussian threats, particularly early on (when Zinzendorf comes up more frequently and is worth more); unforunately that's also when the Prussians are stronger, less distracted by Russia, and you don't have Loudon leading your armies.
So with help from France, caution with your thaler, and by not losing Prag, you can stay afloat financially. Whether your armies can stay afloat is a different matter . . .