SqueakyClean
1) Eat them faster!
2) When you buy them, are they green, or are they ripe?
Perhaps you could buy a few that are somewhat green and a few ripe. Eat the ripe ones while the green ones are ripening.
3) Bananas aren't really ripe until they are fully golden (no green) with brown speckles. Some people consider that to be "too ripe" or bad, but it isn't.
4) Sit them on the counter. If you keep them in a bag they will ripen faster.
5) Once they are ripe or even all brown, if you can't eat them then, you can put them in the freezer, to use later in smoothies or banana bread.
It should be possible to purchase bananas once a week and have them last for the whole week at room temperature, that is if the store has bananas available at different stages of ripening.