There is an aftermarket kit around called Afterburner. It is a frontlight based on a few white LED light strips. However, it involves almost completely dismantling the GBA to install it, a 30 percent reduction in battery life, a washed out and trapezoidal-shaped shadow effect on the display (because it's a frontlight, not a backlight, and it's not originally designed for the system, respectively), and requires some soldering. It's even hard to find one now, because the company that manufactured them has gone under from some legal something-or-other. Of course, you can always get something like these, which just plugs into the EXT port in the GBA and draws power from it to run an LED, which shines at the screen. Simple.
I suppose you can make one if you had the components and skill, but I would advise against it and just get an SP, especially the backlit model (does "Now with a BRIGHTER backlit screen!" ring a bell?), as it is much better than the frontlit one. SP's are only about $40 used nowadays, as opposed to their retail $100; I don't see why you got the original GBA. If you don't plan on doing anything GBA specific, such as GameCube linking or playing Gameboy Color/original Gameboy games on it, you can even go and get a DS Lite/DS-i and effectively get twice the library of games (not the DS-XL, that does not have a Gameby slot.) I would suggest the Micro, but I hate that thing with its tiny screen and its cheep faceplates.
Comparison of frontlit GBA SP to backlit GBA SP
GBA SP at Gamestop