Modder "Bacteria" took a PSOne LCD screen and made something truly wonderful with it: a portable Turbografx-16 system called the "IntoGrafx" that can play both Japanese and American games. It features the standard two-button controller, with turbo switches, and a 5.4" screen. It's a nice compromise between the two existing Turbografx-16 handhelds, combining the TurboExpress/PC Engine GT's portability with the PC Engine LT's more usable screen size. Also, it's red.
Bacteria has posted detailed build notes for this, in case you'd like to tackle this project yourself. If you're not technically inclined, however, you can always just play PC Engine and TG16 games on your PSP.