PokeBank only transfers to gen 6 or 7, or Home.
If you want to transfer from Pearl to Diamond, you need the following:
- Two Nintendo DSes or 3DSes (or one of each)
- Both games (Diamond and Pearl)
(Note: Internet trading has been discontinued for the Nintendo DS, so this is the only way to trade between these)
Insert them into each DS, and in any Pokemon Center, go to the top floor. There will be two places to go to. The Colosseum (for battling) and the Union Room (for trading).
Talk to the lady in the middle in both games and she will take you to the Union Room. Once in there, wait until the player character in the other game appears. It probably won't look like Lucas or Dawn (or Diamond and Pearl, or whatever you call them) but that's okay.
Talk to them and they will be the other player (unless a third person is in your area).
Select trade and who you want to trade in each version. (Note: In gen 4 games, you can only trade using Pokemon in your party.)
This also works in Platinum and HGSS.