T2 is good for the right setup. It is particularly good on a lot of 5/2 boards where the alternative is waiting until at least T4 to donate and you get a strong opener.
It would be extremely powerful on a 5/2 Soothesayer setup:
T1: Soothesayer
T2: Buy donate, pay 2 debt
T3: give curse, gain gold
T4: give curse, gain gold, pay 3 debt
T5: give curse, gain gold, pay off debt, spend $3
T6: give curse, gain gold, buy province.
If you keep a copper, then you can buy a $5 on T5 for added fun.
Another power opening would be a 5/2 Ball -> Tmap -> Donate
T2: Buy donate, pay off 1 debt
T3: Gain 4 gold
T4: Pay off debt, buy a $5
Keeping around a copper will let you buy a $7 on T4; Expand seems like it could be crazily good here.
Feodum would be another power T2 opener:
T1: Feodum
T2: Donate, pay 3 Debt
T3: Pay off debt
T4: Buy a $6
A case could be made to grab a silver on T2, but it would depend on the board how much that would be worth. Say you do that and hit a $4 on T3, that means that on T4 you end with 4S/a $4. That will often be worse than 3S and a $6/5. It would be exceedingly rare not to go Feodum/Donate as your opener on a 5/2.
There are a lot of gainers that would tempt me to mess around with a T2 Donate: Hop (with Nec - end T4 with copper, nec, silver, Hop), and $4; Iw (end T4 with Copper/Iw/Silver/Silver & no debt), Treasure trove (end T4 with Trove, 2 Gold, 2 Copper), and Alms.
Crazy things, like a T1 Inheritance might also come into play. Something like Inherit/Baron or Inherit/Poorhouse could work very well - pay off the debt on T4, grab a village and start hitting 8 on T5.
I could even see very rarely going for a T1 Donation. Say something like Donate (pay off $5 debt), have deck of $5 & pay off debt (maybe a $2 like Courtyard), buy Windfall, buy Donate (trash all but 1-2 copper), buy Windfall. Having a deck of 6 Gold & a Copper or two on T6 is basically 4 provinces by T10-T11. Very few things will be in that league.
While these are obviously extremely good candidates for an a really early Donate, my guess is that you want Donate earlier if you have an option to gain a lot of buying power quickly on the debt repayment turns. I also think repayment over two turns is not so terrible if your alternative is to wait through a $2 turn or buy something, like Silver, that you do not really want.
Mostly I suspect that T1 will be exceedingly rare, T2 will be for power openings & maybe strong gainer openings. T3 - T5 will be the sweet spot, very rarely would I expect to donate after T5.