I would carry a tarp in the trunk. When you gut it, drain the body cavity really well by either picking it up and holding it, or propping it against a tree till it drains. then lay the tarp in the trunk, put deer in and fold tarp edges up and over. Then strap the trunk closed.
I've seen cars with deer across the roof, the trunk, the hood, and in the back seat. Do what ya need to, but I would certainly try the trunk.
-Jake