Continuances are usually within the judge's discretion. I can't tell from your question if the pro se defendant received no discovery at all, or just wants more than was provided originally. Filing a motion to compel the state to provide discovery and asking for a continuance as an alternative would be my strategy. But I don't know how SC works.
I do know that it is very very difficult to win a trial pro se.
My answer to your question is based on the facts that you provide in your question. Additional factual details about your situation could change my answer completely. The law in inherently uncertain and always subject to change.