Mineral spirits should work for this Elizabeth! Dab-don't rub! It will be stinky so try to do it outside.
If the cover is washable and removable, I would wash it adding bleach to the water. You don't want to make it spotty looking.
What is on it?
First remove the cover. I would spray the spots on it with a pre-wash product ( I use the one from Dollar Tree). Let it set to get into the areas that are spotted. Then wash with a peroxide based bleach, such as Oxyclean.
Hi Elizabethmdarby, I would remove it and soak it in a tepid water with a mild soap, check it every half hour and agitate it , change the water when it looks dirty.
Definitely use the delicate cycle on your washer. Dry on low until almost dry. Watch for shrinkage, It can be stretched a bit when not dried completely.
I think the mineral spirits idea might work… But are there other suggestions, since this is a very dark floor stain that’s on the chair cover?