Nothing is as nice as having a professional painter do the job right but if you would like to try it yourself then have at it.
I have done what you are looking to do and had pretty good results using http://www.automotivetouchup.com/ The thing I did wrong was laid down the clear coat too heavy and after a while the clear coat started cracking otherwise I thought the color matched very well.
A mirror like most any is kinda tough to paint and clear coat with a nice uniform coat because of all the areas that you need to hit and not lay on too heavy or get over spray on what you just did.
It shouldn't be hard to paint the mirror and get a nice match. I've done a few and was happy with the results, UNLESS it is a tri-coat (White Diamond or Crimson Red). Then have it done, you'll never get a good match.
Had to repaint because the used mirror I got was kind of gold and my Caddy is Deep blue. But looking at the instructions on Alldatadiy I found out how to replace the glass itself ( problem #1 solved) and then fixed the crack in the mirror case (problem #2 solved) and repainted with a spray can specially made at a nearby car paint store (real car paint not touch up can) with great result both color match and finish. I'm an happy camper now !
P.S. ( Wanted to in all nooks & cranny thats why I wanted to take everything apart )