...but I'm having trouble figuring out what size tire to get since it has both 185/80/R13 and 175/70/R13 on it. By the looks of it, 13-inch tires are mostly trailer tires these days.
Gets some 14" small bolt steel wheels. Dime a dozen in the 14"x4.5" wide, or pay a little more for a 14"x5.5" wide steel wheel. 205/70-14 works well on the 4.5" wheel.
215/70-14 works well on the 5.5" wheel.
Next up, turn those stock caps into frisbees, and get a set of dog dish caps. Good to go.