Dennis --
You should be able to pull the alt. and bench test it at any decent parts house. If faulty, sure you can replace it with a similar unit -- most of these conversions use Delco single wire units but you should match whatever you have. That said, it might be wiring related. Many 12v conversions are poorly done.
My personal view is that the trouble with alternators is that they're 12 volt. (sorry, couldn't resist.) My point is that a properly maintained 6v system is great. Many 12v conversions were done to overcome some issue that isn't the fault of the original 6v system. The faster cranking speed masks the real fault for a while but it doesn't actually fix anything. Just beware of other troubles lurking "beneath the surface."
Hope this helps,
Pete P.
Harborcreek, Penna.