Connie and I have tried several times to grow bananas here, but have never been successful at it. They do great the first year, but never seem to recover from the Winter months when it kills them back.
Maybe with global warming, before we die we will be able to grow more of the really tropical stuff. I would love to grow coconut palms! Once when we were in Sanibel, we found some coconuts laying on the ground that were already sprouting plants from them. We brought a few back home, and tried to grow them, but it only took temps in the mid 30s to kill them. They don't like cold even a little bit.
But it isn't necessarily only the tropical stuff that I can't seem to grow. Watermelons have slapped me around every time I try to grow them. And I thought they would be easy. Plants do well, vines well leafed out, flowers look good, and small melons will form. I water them about once a week, give them fertilizer, and set up "bunny blasters" to keep the deer from grazing on them. Invariably, the melons will either split open on their own, or get a black spot on them that just spreads and destroys the melon. I have tried MANY different varieties, all with the same results.
