We drive a manual, so I can't give any first hand experience. As a general rule:
Using Autoeurope would give me more confidence that they will have an automatic. It is a large consolidator and they carry some weight within the industry. I have tried to book in a smaller venue and they have come back and said what I required was unavailable. That was done at the time of booking.
The other problem with smaller venues are restrictions on opening and closing times. (Particularly if you are picking up or dropping off on the week end.) Once again, Autoeurope will not book you with a place that won't be open. (exception will be returning the car. You are allowed to return your car when they are not open at some places...but these are usually large places and/or airports). Even then, Autoeurope warned me we would be returning to a place that wasn't open at that time. I had to agree to that before booking.)
Since you have already booked a car with Autoeurope, I recommend you call them directly if you are thinking of adjusting your reservations. (much easier than canceling and re-booking) They are very helpful and certainly can answer these questions with more experience than I have.