Depending on your route to your rental:

If you travel via Marigot there's a market in the Howell Center (right side of main road on your way) SUPER U. Ample parking, need a US quarter to get a shopping cart. Need to have your own bags.

Further on this route after Grand Case near Cul de Sac in Hope Estate (right side) is another store. (can't remember name) I believe you'll still need your own bags.

Route from airport thru Simpson Bay is Grand Marche . Cab driver will know where any of these store are. There's a waiting charge for the cab.

I'm sure others here may have other suggestions of smaller stores.