Your best bet is to use AirBnB, a lot of times you can make reservations 6 months or more ahead, which guaranties a place for those dates so you can get cheaper tickets and get vacations appoved, etc.
However you may get bored and may end up with an incorrect view of Puerto Rico if you just spend that much time in a single area. I would suggest 1 week in different areas of PR, so multiple AirBnB places would be the way to go. There is heavy traffic in PR and driving from one part of the island to another can be 1 to 4 hours each way. Best stay in the area you want to explore.
Rey