According the the NM Railrunner website it runs 5 Saturday trains between ABQ and Belen and 2 Sunday trains. Times might need adjustment to match Amtrak. Of course commuter trains don't wait for late trains so the Amtrak bus might be a better option.
NM Railrunner Weekend Schedule
Another catch is the RailRunner station is not on the Transcon. This means some conection would have to be made in Belen.