No, from what I have read, no persimmons, avocados or rhubarb (among other things, obviously). I would not feed persimmons to your bird because rhubarb and avocado are HIGHLY toxic to them and to see it lumped in with these on various lists is concerning and not worth the risk IMO.
They can poison horses due to tannic acid....I am not saying people have never done it, but there are certain toxins in certain substances that build up over time or harm organs, so I don't see the necessity in attempting something risky.
They also contain something called shibual (a tannin)which can help and hurt people and lead to bezoars in cats, birds and other animals (it's a blockage).
There are so many types or persimmons and their ripeness varies (and changes their contents as well) SO, I just would be uncomfortable with it.
There are also some reports of persimmons linked to botulism .
I don't feed my bird honey of any sort either...so even if it was just the botulism risk, I'd say no, given the tannin risk on top of that.
I know of some people who do feed them to their birds. I just don't think it is a good idea, give all of the alternatives and the data suggesting that they may be harmful in some circumstances...Heck, think about people who drink too much or take drugs and survive-- it's not like everything kills an animal right away...
It's long-term that has me worried.