Singer (made in USA) should be an SAE thread.  Could be fine or coarse thread pitch.  My local ACE hardware has a tremendous selection of screws, bolts, and such.  Lowe's stocks stainless steel machine screws in size 4-40, 6-32, and 8-32.  A hobby shop that caters to radio control enthusiasts will have small screws in both SAE and metric threads.
 
	Grainger, Fastenall, and McMaster-Carr also stock a wide variety of hardware.  If you can identify the size and thread pitch, a gunsmith may be able to help.