Do the following and you are guaranteed to find Slimes:
1. Load your game on Easy Difficulty (or any difficulty other than Peaceful)
2. Dig down to level 4 (right above bedrock)
3. While at level 4, did a hole 3 blocks high and 100 x 100 across.
If you do this, there is mathematically no possible way you will not obtain slimes. In fact, chances are slimes will start appearing long before you are done (especially if you go back up the surface now and again for a smoke).
Things to keep in mind they will spawn in whatever light level so make sure you place some torches don't need them pesky creepers walking up on you. The other thing to remember is to NOT hit them with a sword punch them, this may have been fixed but they
used to not drop slime balls when attacked with a sword.