Yes, you can.
You do it by using the pal park transfer function.
(after beating the Pokemon league)
You need to trade one from Diamond, Pearl, or Platnium.
I'm pretty sure that the only way to get another starter Pokemon in Pokemon diamond is to go to the Global Trade Station (GTS) and trade with someone.
You have to get Piplup for the starter Pokemon and level him up or trade for it.
trade
You have to choose it as your starter Pokemon or get it in a trade.
The only way to obtain a Turtwig in Heart Gold and Soul Silver is to trade it from Diamond, Pearl, and Platinum. Sadly, you are forcing your friend to trade their starter Pokemon.
You have to trade at the GTS
You must choose it as a starter or trade over from peril.
Trade with another Pearl or Diamond.
Piplup is a starter Pokemon if you didn't choose it have a friend trade you it.
Either have it as a starter in Pokemon Gold, Silver, Crystal, Soul Silver, or Heart Gold. In Pokemon LeafGreen and FireRed you'll need to trade a Pokemon for it. Also in Pokemon Sapphire, Ruby, and Emerald. In Pokemon Diamond, Pearl, and Platinum you have to trade a Pokemon for it. Hope this helps!
You will have to trade it with a friend or GTS. Or, you could bring it to your game with your Heart Gold, Soul Silver, Diamond, Pearl, or Platinum with the PokeTransfer Lab.