Probably the easiest cure would be a one wire GM alternator conversion, and it would most likely end up being the least expensive too if you source your own parts instead of buying a kit. THe brackets are fairly simple to make if you have access to a drill press,welder, and some metal to make it from. The alternator could easily be purchased out of a U-Pullit yard for $25 or so. The kits are nice in that everything is all ready to install with instructions but they usually are way overpriced for the reman alternator they include.
That said, who rewound your generator for 12 volts? Did they also sell you a 12 volt regulator to match it? If it was recently purchased, it would behoove you to bring the jeep back to them to test out.....seems as if something in your generator/regulator/wiring is amiss. Realize even a 12 volt generator is not going to give you the amerage that a good alternator can, but it should at least keep your battery charged and the ammeter on the positive side of the scale most of the time. The simplest cure may be just to polarize the system, and your rebuilder should be able to tell you how to do that in a few minutes. There are several different circuits for generators and regulators so I won't attempt to explain that. If you Google VERNCO tech tips, he has a good section on generators.