Quark's

From the Memory Alpha wiki:

He did not require sustenance, but occasionally ingested semi-organic nutrient suspension in a silicon-based liquid medium to lubricate his biofunctions. (TNG: "Deja Q") Though capable of consuming more traditional food and drink, Data had no sense of taste and therefore tended not to bother eating. (TNG: "Hero Worship")

So, you could probably derive some of the organic components from bananas, but generally no. He's not really banana-powered.