I was stuck with this same question a few weeks ago. I framed my deck with angle aluminum and I originally planned on cutting the deck and using the cutout to make a carpeted and hinged lid. It was going to require modifying my framing to support the closed lid. After a lot of thought about it, I just didn't think I was going to be able to do it that way and make it as sturdy as I would like and have a door of any size, so I ended up buying factory made aluminum hatch lids and just cutting a hole and dropping them in. They are very stout and can be carpeted over, so all you see is the frame. I spent quite a bit extra doing it this way (more than I was planning on), but I'm more than happy with the results.
These are the hatch covers that I used:
https://www.cabelas.com/cabelas/en/templates/links/link.jsp?id=0001528010645a&type=product&cmCat=SEARCH&returnPage=search-results1.jsp&QueryText=hatch&N=4887&Ntk=Products&Ntx=mode+matchall&Nty=1&Ntt=hatch&noImage=0
They have some heavy duty plastic ones for a little cheaper too...
https://www.cabelas.com/cabelas/en/templates/links/link.jsp?id=0053189019707a&type=product&cmCat=SEARCH&returnPage=search-results1.jsp&QueryText=hatch&N=4887&Ntk=Products&Ntx=mode+matchall&Nty=1&Ntt=hatch&noImage=0