Visit a special gibbons rescue resort called Gibbon Rehabilitation Project on Phuket Island, which does a stunning work, returning once captured tortured and abandoned gibbons back into the wildlife. The major source of income is the Project's shop, so be sure to buy something there before you leave.
Although you are not really allowed to see the gibbons closer than two meters, this is the only place where you can be sure that the animals are well maintained and overall happy. The mating season occurs every month of a year, but most babies are made throughout March. Therefore, you have a pretty big chance to see the cutest newborns in October!