You should know how to powershield on the run, and wavedash out of shield to continue closing the gap. Preemptively approach when it's safe to do so, and don't be dumb (for anyone reading this)- Roy doesn't have a lot of options so know how to use what he does have without getting yourself punished. Use landing fair into grab/dtilt, or to beat his nair (if he's smart enough to be using it), and just perfectshield (and grab), dash, or wavedash away from dair since you can't answer it. I doubt he'll be using run-up shine-turnaround SH bair, but if he does, you should be ready to Counter or shield and get a grab.
Grab, Nair #2, B-air (mid % or higher, in-combo), those are like your other main moves. Jab helps with combos but don't use it too early. (Sweetspot) Dtilt as often as you can and extend the **** out of it, try to turn every touch into a 4 or 5 hit combo. Don't drop your tech chases. Try to avoid platform stages since personally you prefer the ground. Pretty much just learn your moves and fight him. Most importantly try to tech[/roll] unpredictably, and try not to get hit.. I mean, you're going to, but I'm just saying try, since Roy can't really afford it, lol. And another thing, listen to the guy above me. Don't make it obvious that you're trying to camp the ledge but craftily lure Falco to it. Falco is too godly at center stage so try to abuse his main weakness which is recovery. When he up-Bs to ledge use SHFFL Dair through it to kill him. When he side-B's, you use Jab to kill him or side-B, depending on if you want to spare him just to **** around and then unsave him. This matchup is so much better in SDR and PM, lol.. but I like playing it in vanilla Melee just to see how well I can do
Oh and alternately, you can skip all of that and try moving your CSS coin one space to the left before you press Start at the character screen, this is the best known method of beating Falco as Roy