You would likely need a new index compatable rear derailler, chain and a new index compabale freewheel to get good index shifting, at which point it likely would have been easier/cheaper to just start over with a better bike. If you do go this route, go ahead and get a 7-speed freewheel and shifters & chain, no compelling reason to stay 6-speed and the 6-speed parts will be even harder to find and cost just as much (if not more) than 7-speed.
Good thing about friction setup is that it allows for a simple upgrade without costing too terribly much and friction shifting requires less maintanence and works better than a neglected index setup.