Money trees are still possible to plant. According to the Animal Crossing wikia, they do appear in New Leaf. You need to bury a bag of money with a Golden Shovel in order to plant a money tree, and you then get a chance that the Money Tree will grow based on how much money you planted in the ground.
As the wiki states,
After the tree is grown, if it blooms there will be three bags of the amount of bells you planted or 30,000 Bells bags, whichever is lower. The tree will only bloom, and thus produce money, once.
This chart from the same wiki shows you the probability of the Money Tree growing, along with the expected reward from the tree.
Note that it is on average never profitable to plant money trees.
