D.N.
Do you make the lunch the night before? My kids used to take lunch and they would put the banana in their bag the night before and it would turn brown faster. the gas a banana naturally creates turns it faster especially in a bag. Don't put it in his lunch bag until right before he leaves. If this still happens, buy bananas just slightly (very slightly) green so it does not completely ripen to brown. A brown banana is actually sweeter and completely ripe versus what we consider a nice yellow banana.