Thanks, both of you!
I guess I should have clearly stated that I'm looking to NOT used any canned products. Pineapple, it's that plain old sauce that I'm trying to make for myself, because the canned is giving me a reaction. Amma, I just despise canned tomatoes.
So I'm looking to start with fresh tomatoes, though for some reason, I can use Spice Island's Italian Seasoning with no problem at all. I just don't know what I'd add to fresh tomatoes (I assume I'd chop them up and boil them) to make it end up sauce and not mush.
I think I'm just going to give up on the bananas. Your suggestions are good ones, but every time I think of making any of them with overripe bananas, I just get queasy.