There is no simple way to get standard video signals directly into or out of the PSP's LCD. It is not just a matter of converting the signal to digital or analog, the timing requirements of the LCD are also completely different, and correcting this is not a trivial issue. You would still need some powerful programmable logic to buffer and rescale a full frame to make it displayable.
If you are looking for a small display that will accept composite video input, try the 5" PSOne lcd that is commonly used in portable console hacks.