I just checked with McMaster-Carr and they do have round leather
belting.  Search for "Leather Round Belting" to find it.  As far as
joining the ends together just drill two small holes for the hook and
tighten the hook with pliers.  If you don't like the clicking then
join it together with dental floss.

Don Teach - Shreveport Music Co.
Shreveport, Louisiana