What are the appropriate MOS codes for all branches for Delivery Drivers and Special Delivery Drivers?

The only MOS even REMOTELY close to those is 88M, Motor Transport Operator. I do not believe the Army has what you asked about. Of course, this brings on the question of why you're asking.

I don't think that's a thing

What? So either you are looking for something generic like motor transport or you are looking for something like Mail Courier or Postal Clerk. But you can do a web search for those MOS's for each respective branch. But if you clarify your question you may get more support from the folks on here.