While you can't get Croagunk directly, you can get its pre-evolution, Toxicroak, in HeartGold via trading. This means you'll need to trade with someone who has a Toxicroak from a Gen IV game like Diamond, Pearl, or Platinum.
It's worth noting that you'll only be able to trade Pokémon that are in both HeartGold's and the other game's Pokédex. Since Toxicroak is not in HeartGold's Pokédex, you may need to trade with someone who is willing to trade it via the Wonder Trade feature, which is a random trade feature.
While you can't get Croagunk in HeartGold, there are plenty of other cool Pokémon to collect and train!