Like others have said, September is a an easy month to rent for a week or two. I am renting for 8 days this coming September.
Usually
VillagersHomes4Rent.com works for me...but not for my upcoming rental. A couple of weeks ago I emailed one landlord - never heard from him. I called another landlord and left a message on her voice mail -- never heard from her.
Then I tried v r b o . c o m (leave out the spaces in between the letters), and the first landlord I emailed called me back within 24 hours, and my rental for September on the Historical Side is booked.
So I am not discounting
VillagersHomes4Rent.com, it just didn't work for me this time. It could work very well for you as it has for me in the past.
As far as airbnb goes, I did use that site when I stayed in The Villages for a couple of days this past New Year's weekend. It was my first time using airbnb, and I was happy with how the rental turned out. That site may also work for you. it seems to cater to the shorter stays (2 weeks and less).
And sorry to go off topic, but just a rant...if you are a landlord, be professional and return a prospective tenant's email or phone call, even if you cannot rent your home to that person for whatever reason. Just my two cents.
Good luck finding a rental in September. I am already counting the days until I return!