Nothing much cheaper or better suited for your situation than ANNUAL not PERRENIAL ryegrass. Prep the soil well and it will germinate in 5-7 days and if you feed and water it will look decent for exactly one growing season. Just be diligent about mowing so it does not go to seed and broadcast itself all over the place where you do not want it. Not sure where to get it standalone this late in the season but do you have a real nursery, feed/seed store, etc. around? My local, not box store, hardware store use to carry turf seed open stock this time of year. Might be able to get it online?
Worse case? Look for contractor blends and check the label on the back. Such blends will have a high percentage of annual rye but unfortunately other turf grass seed you probably don't want if the plan overall is zoysia.
Worse case? Look for contractor blends and check the label on the back. Such blends will have a high percentage of annual rye but unfortunately other turf grass seed you probably don't want if the plan overall is zoysia.