I didn't notice them at first, but when the people ahead of me in line raved about the American persimmons for sale by Coyote Hill Farm at the farmers market, I decided to try them. I had had Asian persimmons when we lived in California but had never tried the native American ones. These were much smaller, maybe around 1 1/2 inches in diameter.
In general, I have to say I'm not convinced they were worth it. Each fruit had several large seeds in it, and while the flesh is very sweet, it's sticky and there isn't that much of it. That said, I know some people love persimmons, so if you find them and don't mind the fuss, give them a try.
After we ate a couple straight, I decided to try to separate the seeds from the pulp and do something with the pulp. It wasn't all that easy. I tried putting them through a food mill, but the seeds were large enough that they got in the way. I eventually ended up pulling the seeds out with my fingers and then putting the flesh through the mill to puree it. That worked reasonably well, but I wouldn't want to do it with a large quantity (I had a pint or so of fruits). This yield around 1/2 to 2/3 cup of puree - though it was really more the consistency of paste than puree.
Since the amount of puree I had wasn't large, I decided to mix it with some applesauce. I did about a 1:4 ratio of persimmon puree to applesauce. It was quite tasty, and turned the pale yellow applesauce a pleasant pale orange color. I think this might make nice fruit leather as well. You could certainly go heavier on the persimmon in the mix if you had enough.