When you're looking at renting an all wheel drive vehicle, it can be hard to a) find
one that isn't an SUV and b) to find a company that will allow you to either reserve that vehicle or option specifically. See our Vehicle Guide
It's rare to be able to book a specific vehicle or feature that is not standard online and rarer still to find a car rental company website that lists all makes and models available. You usually see statements such as ... Chevy such-and-such "or similar".
What I would suggest to you, is that you contact several locations in your area, directly. You can usually find local phone numbers if you go to yellowpages.com and search for car rental for your specific city or town, or by searching a specific car rental company website for location information for your preferred city/town. When you call, ask to speak to the manager on duty.... and get their name!
Tell them that you're interested in renting an all wheel drive vehicle, and ask them if they carry any all wheel drive vehicles that aren't SUVs, and if so, ask them if you make a reservation directly with them (over the phone) would you be able to get a confirmation (in writing -- ie email) that you could reserve in advance, and guarantee a vehicle with all wheel drive.
You can also check various car rental company websites directly (avis, budget, hertz, enterprise, etc) for your preferred city, dates, times, etc and look for vehicles that may be all wheel drive, but not in the SUV category... instead of looking specifically for wording in a category that directly states that you would be renting an all wheel drive vehicle, try looking at a category that may also contain that option...look at the makes and models available for premium classes, specialty cars or even crossover vehicles.
The Basics of Car Rental
Car Rental Phone Numbers