There is no reason many different good primer sets can't be designed for GFP. You can check the primers you researched to make sure they match GFP sequence if you are not sure what they are for. It's best to use primers where they show actual results, and give PCR conditions (a primer may be excellent in one set of conditions, but not work in other condtions).
Here are some primers I designed for eGFP (enhanced, some mutations different from old GFP, I'm not sure if they are in the primer region) [Edit: I checked. The primer sequence is different for original GFP.]
221 bp product.
Used in Roche LightCycler SYBR mix.
95C 10 minutes.
Cycle: 10", 6", 15"; 95c, 63-60C(Touchdown. Delay 6 cycles at 63C, then -0.5/cycle until 60C.), 72C
Melt curve program.
(This is a touchdown program. It worked OK at 60C anneal (no touchdown) but didn't look as perfect. Probably would work better at single anneal temp 61, 62 or 63C, but I haven't tried it.)