I live in the north so I don't plant it outside. I have a coconut that was sprouted about 10 years go. The center of the largest leaves have gotten brown which isn't good thing I know. I think it's probably going to die but it has a small baby off to one side. Please advise how you would handle this plant. I would at least like to save the baby. Kathy Lancy
You actually have kept your Coconut Tree alive much longer then most survive in a potted environment.
I can find very little information on the propagation of a side shoot.
Without seeing what the shoot looks like, I will assume it is similar to a Banana Tree.
I would follow the directions in the link below.