You will need to strip the existing oil base stain. Use an injectable stain stripper and a pressure washer. This will remove most of the existing stain and open up the wood pores for good penetration of the new stain.
One more thing; use a very good solid stain. Skimping here will cause many problems. Also consider using an emulsified oil stain instead of a pure acrylic. Check with your local paint store for availability.