Tonneau covers with no clips

Sorry in advance for my annoying question to read lol.

So my girlfriend has a 2004 Tacoma 1st Gen. I'm looking to buy her a tonneau cover. Preferably a tri-fold. I did as much research I can. I did order one but had to return it. It was a tri-fold with clips so no tools required. But the issue we ran into is that her truck bed doesn't have that gap on the side (sorry I don't know the terms for trucks). Basically the clips will hook onto the side of her truck in the gaps, but she doesn't have that, it's all flushed. So what I'm wondering if there's a tonneau cover that don't have clips and that will work with her truck.

I've also attached a picture of the trunk of her bed.

 

Don't know of any that will work with that type of bedliner.

 

Yeah thats what i assumed, couldnt find any that dont use clips