I live on bananas for the potassium and my stomach. I eat them everyday, so I have to keep them for long periods. The old myth was to Never put bananas in the refrigerator; It almost floored me at the store when the woman in charge of produce went seriously bonkers, and insisted bananas rot in the fridge! My grandmother told me long ago, the Chiquita banana commercial was wrong.
Yes, the skin will turn black, but the inside stays nice and firm for a long time. At least 2 weeks. I buy some a bit green and some yellow, and eat what I want in the first day or 2. Then I take the ones that are almost yellow, before they get too near eatin'-ripe, and wrap them in the plastic grocery bags from the store. Not tight, just so they are covered. Then put them in the crisper (I use one crisper for bananas only).. and take one out as you need it. Keep covered. They don't get as black, and stay lovely inside, longer than if you just plop the bananas on a shelf.
After all, they ship green bananas to our markets in refrigerated coolers from all over & South America.
My health has vastly improved with my banana diet this past year, and I love them as well. Shine's suggestions are excellent. Healthy yummies.