It's a fascinating question. He cannot stand to share the spotlight. He is a novice, so any seasoned politician brought in would have to be able to show gravitas and not shudder noticeably in public when Trump says stupid things. It would have to be someone with no ambitions beyond being Veep. Trump wouldn't stand for someone that may want to supplant him, and no serious politician would hitch their wagon to him knowing he'd flame out eventually.
Some lower tier governor whose name I can't think of is the most likely choice.