Sub Placement for my Convertible...

I have a 98 V6 convertible that I have as my daily driver and I want to throw some subs into her. She has the mach 460 stereo system in and the factory door speakers I blew a while back and havent found 6X8's that will cut it for me. I was wanting to throw in two 8" subs but seeing that I have a convertible I dont want to get a box and put it in my trunk I already have zero trunk space i dont need to help that any. So I was thinking about cutting two holes one on each side underneath my back seat. not only would it look great but i wouldnt lose a bit of space in doing this. My question is if this would really work as far as sound quality goes? I wanted to cut the excess foam out of the seat cushion and run a piece of particle board or something and i was hoping would that make a make shift box? Maybe if i cut small holes under the carpet beside the speaker to let some sound escape? I am an amature at stereo systems and how the sounds work. All the fabrication and making everything i describe work isnt an issue i can do all that without a hitch and can hook it all up just fine. i just dont know if the sound quality of the two 8's in my make shift box will be worth my time or not. Also would the stock amp run the new subs or would i need to replace that with an aftermarket two. i know its a proprietary system and an absolute pain but still just wondering. Thank you for the interest!