Just to add, use an oil based primer first. A spray can will work just to prime over the stained portions of the ceiling. If you paint right over it without primer, the stain will bleed through. As other said, flat paint is best. Matching however is going to be a nightmare. You need a flat sample to get a good match with a color sensor. Painting the whole ceiling is the right answer, but go ahead and give matching a shot. You'll have to prime first either way, and maybe you get lucky. If it's too noticeable, you can always just finish painting the rest of the ceiling.