Lake City is the primary supplier of M193 to the US military. Lake City is currently operated by Federal (under Alliant TechSystems ownership), and Federal supplies M193-class ammo to the civilian market as XM193.
Winchester M193 was formerly available commercially in Winchester's budget military line. The model number was Q3131 and it comes in a white box marked USA. This ammo was discontinued in 1999 as Winchester/Olin handed off operations of Lake City to Federal/ATK.
Another good source is Israeli Military Industries (IMI), the sole supplier of ammo to the Israeli Defense Force (IDF). IMI makes M193 and they also supply their M193 as a subcontractor for Winchester, under Winchester's model Q3131A. IMI is approved to supply the US military with ammo and it is often used when troops are in the region, to save shipping costs.
Other M193 is commonly available as surplus from various importers, though that ammo is obviously not new-production. A recent example is the 1980's South African "battle-pack" ammo that was available from a number of sources. This ammo comes in 30-round boxes, packed 10 to vinyl sleeve. It is hot-loaded ammo that appears to be M193 spec.