I don't think worn coil stops would cause the problem you have.
usually the issue is the mechanism is gunked up. Can you easily pull in the coil plungers with your fingers and get a crisp increment of the numbers without feeling resistance besides the initial get-it-moving? if not, time to take the register apart, clean and use a modern thin lube to reassemble.
see http://bingo.cdyn.com/techno/overhaul/magic_ring/replayreg.html - tho that page probably needs some editing for clarity ("editing" = complete rewrite).