Place the device out of site - perhaps in a drawer. Then, play soothing music, light some tropical candles as to make the banana's feel at home, and have a calm discussion with them. Explain that you don't love the device more than them and it will never replace them. I suggest you refer to this site for further help. http://www.ehow.com/how_4890194_deal-with-confrontation.html
Gather all the bananas around the table. Try to figure out who their leader is. Then ever so slowly peal it and set it on the table. Tell the bananas that there is going to be an adjustment in attitudes, that things need to get back to normal. Then in a swift motion, use the slicer on the ringleader. Then without saying a word, get up and walk away, leaving the bananas to stare at their once proud leader. Things will return to normal real fast.
I have found it is best, at least at first, to pretend that you have not noticed that they are incommunicado. Attempt as well as you can to appear "normal." (Whatever that means). If they persist in their pique, eventually offer a small but meaningful token of rapprochement. (Only you will know what is both meaningful, but small: use discretion). If that doesn't work, try playing the Purple Dinosaur thingy. That'll provoke the petulant little ingrates.
In some cases, the presence of other bananas can cause some younger bananas to ripen faster because of gases released by the other, older bananas. I would recommend allowing the bananas to ripen before trying to talk to them again - as they grow older, they should become more laid-back and therefore will forget this silly squabble. However, I also agree with Christa S. in that this implement should be out of sight of the other bananas, as they may relapse into giving you the silent treatment after you have ripened them if they see that this implement is still around.