Write an article based on this "Search for caves below the 40th layer. Add torches to the cave. Clear out a 16 by 16 by 16 room. Create four one-block high platforms. Retreat at least 24 blocks away from the spawn area. Wait for slimes to spawn."
If you aren't able to prompt slimes to spawn in a swamp biome, you may have more luck underground. Slimes spawn in caves located in "slime chunks", which are 16 x 16 x 16 block areas. You have a one in ten chance of coming across a slime chunk. When below layer 40, slimes can spawn in any light situation; adding torches will both make mining easier and prevent other hostile mobs from appearing. This constitutes a chunk. Slimes won't start spawning immediately while you're here, but you may be able to force them to do so by adding platforms. These platforms should be stacked on top of each other with three blocks of vertical space between each. Having these platforms increases the possible spawn area for slimes. As with the swamp biome, slimes won't spawn if you're 24 blocks (or closer) away from the spawn area. If you don't see any slimes within a standard night and day cycle, you'll need to find a new cave.