You have to kill a tree in order for it to create a patch. Then, you can tend the patch and then plant a bean to make a new tree. If you need to do this for a quest, let me know and I will supply :-)
Patches in the wild are almost nonexistent. If there is one, somebody will come along and plant a tree shortly. I know I do if I find one. You will have to poison trees to find one.
Jello's Landscaping Service would be happy to poison some trees for you, so long as we retain exclusive rights to clearing the dead tree and tending the weedy patch once.