Good Morning, we rent for 3 months and have done so for 7 years in the Disney area. We have helped several folks to find monthly rentals and happy to give you a few hints.
Plan A. Use VRBO and search communities and homes that appeal to you. Be sure to put in your full one or two month dates at the top and if just the two of you I would put in two bedrooms plus. Then in the first home that you want to contact put a message in the box that introduces you to the owners and give them a budget for your month. I suggest a note like this: you can substitute relationships and number of guests as appropriate.
"Hello, my spouse and I recently retired from our careers in XX city and state. We love the Disney area are looking to spending a warm 2 months in your area. There will be just the two of us and we will treat your home like it is our own. The benefit for you will be minimal utilities, minimal wear and tear, and no cleaning costs.
Our budget for the two months is $XXXX per month to include all utilities and tax. Thank you for your time."
I would not hesitate to send this to all the 2,3, or 4 bedroom homes that you find. One huge caution. This is very late in the rental process for this year, there will be very few homes available that do not have at least a few weeks rented in this two month period. For great results next year, use this model starting in March or April for the next winter season.
So, it will be rare right now but you might get lucky. The web site should filter the homes that are not rented for the full time but you might get a note back from an owner whose calendar was not correct.
As for budget, I would suggest putting in about $1500/month. That is reasonable, includes everything, and is not what the owner gets by the week but is sure better than nothing. My only concern is the quality of home you may find this late in the process. If you get some offers, I would ask for references from recent renters.
Plan B would be to go through a real estate company or management company but I guarantee you the prices will be higher. This might be your only option this late in the year. I really have no recommendations for a good company to do this. Maybe someone else on this board will have a suggestion.
Plan A is a lot more work on the internet than just contacting a management company but usually is much better deal financially...
Good Luck, Ted