all online parts dealers show just the rings as 20-108-04-S
BUT, Kohler's online parts catalog and breakdowns show them as no longer available and to use, 20 874 01-S which is a new Piston and ring set.
Your in trouble according to Kohler Plus the PN is 20 874 01-S which is list as NLA.
Besides Kohler doesn't have any OS pistons and/or rings listed for the SV590. You're struck with a 94mm setup which if the cylinder is worn over 94.073 mm (3.704 in.) it is new short block time.
Also the cylinder can't over the following either:
Max. Taper 0.05 mm (0.002 in.)
Max. Out of Round 0.12 mm (0.0047 in.)