If it's all the same as the 258 in a jeep, then it's a Carter carb. The problem w/ them is that the body wears out where the rod goes through that holds the plate in the throttle. The carb body then leaks below the throttle plate. These can be drilled out, bushed and repaired, but then you still have a carb that has a problem idling because the idle tubes are too small and they get clogged.
First thing you can try is to clean out the idle tubes. If you take the top of the carb off, you will see them sticking down into the carb body. I think a small plate and screw hold them down. Seems there is a check ball in there too, so be careful removing it. But, get the tubes out and ream them w/ a guitar string, or piano wire or something similar. Should help a little.
That said, the MC2100 is a very popular swap. It's a good, cheap carb. It's easily rebuilt, and when running right, is almost as good as fuel injection. You are looking for one that has a 1.08 bore. They came on various size motors and the bore varies.
Again, I dont know how your Eagle compares to a CJ7, but from 83 on they had a computer controlled carb. This too messed things up. You can bypass the computer though, which helps the carb run better. Search for "Nutter Bypass" and you should come up w/ instructions.