Well, the only way you can get it is through Croagunk and Toxicroak - you just need either:
- An item stealing move
You can easily get Pokeballs, of course. $200 at the Pokemart. Woohoo! x)
However, for an item stealing move there are a few, such as:
Thief (will not work if your already holding an item)
Covet (will not work if your already holding an item)
Trick (it will switch your item with the opponent's, not steal)
And that is all. :3
When you click on the links, you can see which Pokemon knows that move.
You can either catch the Pokemon or take the item from the Pokemon, if you wish. Remember, only Croagunk and Toxicroak have these items. It's also a 5% chance it will appear on the Pokemon. (1/20)
If it becomes all too annoying for you (don't worry, it's okay to give up) then you can steal the Black Sludge from Trainers. Unfortunately, though, all trainers that have the Black Sludge are in HeartGold and SoulSilver. If your willing to trade, all the trainers are on this page.
Good Luck - Hope I helped. :)
Sources: All linked pages