Not sure what a "trunk cover" is. If you're talking about the plastic panel on top with 2 side wings, that should not keep you from using the top. I've seen cars with that panel missing completely and the top worked fine.Red 2007 GT 3.5L, with 162k. Trunk cover and wings are busted, like so many others, so I can't open the top for now. But she's fun nonetheless.
If you're taking about the rollup "shade" cover inside the trunk, you can get those on ebay. You can also cheat by sticking something in the right side end to actuate the switch. Just don't put stuff in the trunk above the shade level or something will crunch