I want my yellow roses made with royal icing to have a red outline on the petals.  What would be the best way?

You need to paint a stripe of red colouring on the inside of your icing bag and coupler, and make sure when you add the tip to the coupler the thin end of the petal tip is aligned with the red stripe. 

Or, make your roses, let them dry, and dust with petal dust.

AI striped a bag with red icing on both sides of the bag, but it mostly came out red. So you are suggesting I stripe one side of the bag with food coloring?

Yes, and try to line up the thin end of the tip with the stripe. Not too heavy on the colouring though otherwise yes, it might all mix together just before squeezing out. I wouldn't fill your bag too full either, I would use a few disposables and lots of trial and error. Still would be quicker than dusting them afterwards though, once it comes out of the bag properly.