I repaint bikes quite a bit. Get a quart can of Benjamin Moore Advance Gloss in whatever color you like. Use a 3/4" flat art brush, 2.99 special at Michaels craft store. Scuff up the paint on the frame with some fine sandpaper. Wipe it down with mineral spirits or whatever solvent you have on hand. Then go at it with the brush. I hang my frames by the rear dropouts from the ceiling in the basement. Takes about an hour to do one coat. 2 or more coats is good, drying overnight between coats.
A little rubbing compound and a coat of wax when all is dry and you're good to go.