I need to know what kind of riveting machine is the best to make holes
and punch pegs into a leather belt in order to connect the backle.
The distributors with their phone numbers (andif available, their
websites). I'm looking to start a website selling men and women's
apparel leather belts. Please include your sources.

Is this a hobby?  Hand punches and rivet sets should do. Get a nice big vice
to hold the rivet anvil.

Tandy might be a place to look.

If your in some production situation  Flexibility as to sizee color
shape will be important.  New England and the South is where a lot of
leather shoes and belts were made. Leather related toolmakers are
likely still there.