If it's indeed a Challenger or a Challenger II and not the more recent Challenge<--note the lack of an "r", the best idea would be to retire it and buy a new Buckmark.
Challenger and CII magazines are all but non-existant.
Sure, lots of on-line places claom to have them but when you talk to them they mysteriously have been recently sold.
http://www.browning.com/products/catalog/firearms/buckmark/buckmark.htm
If it looks like a composite of the Buckmark Challenge and the Buckmark plus,,,Challenge thin pencil barrel and the Plus frame w/ a larger Browning medallion more centered in the wooden grip,,,with deep "too die for" bluing, it's probably one of the older Challenger models.
I came this close --><-- to buying one a few years back at Dicks Gun Room (my local dealer) for $125.00, in As New in Box condition. The only problem with it was that it didn't have a magazine,,,the reason it was so cheap. The thing was goregous and I really wanted it, but the salesman (Gary) was quick to point out the lack of a magazine.
Don't give up hope though (if the above applies) since every once in a while odd ball things like this pop up at gun shows. FWIW, I have a couple of older less well known guns that I've had to retire because parts are so hard to find it isn't worth the risk of shooting them anymore.