Slimy Tree are added by Tinkers' Construct that may be found atop Slime Islands.
Slimy Leaves may drop Slimy Saplings which will grow new slimy trees. Slimy trees can be naturally found on slime islands. Slimy Leaves may also drop Gelatinous Slime. Instead of 4 wood planks, trying to craft slimy wood gives you 4 slime ball. Bonemeal does not work on slimy saplings in survival mode, only in creative mode.