You can use either of the two parts numbers listed below. The filters are identical except for their length. Many engine configurations have enough space to accomodate the the longer filter, but measure your old one first if you're unsure. Most home centers (Lowes) carry both.
12 050 01-S
52 050 02-S
1.6 quart
KOHLER 1205001
SAE 30 or SAE 10w30 weight. I recommend full synthetic.
The Amsoil / Wix # is 51056
Wix #51040 is a direct replacement.
PH3614
51348
Acording to the Fram Oil Filter reference guide, Kohler 12 050 01 s can be replaced with Fram PH8172.
12-050-01 may be a better number to search oil filter suppliers for a substitute. The Kohler oil filter 12-050-01 was superceeded to 12 050 01-S1. Fram still has the old number and it crosses to Fram filter PH8172
The Fram number is PH7575 or PH3614
Looks like a PF53
Purolator L10241 (or PL10241)