It took awhile but my husband finally finish the baby's dresser/changing table with a some help from my step-dad. Click here for instructions on refinishing a dresser.
Here is a photo of the dresser before the sides where painted the darker pink:
And here is a photo of the finished dresser:
I ended up buying two new Pottery Barn Kids chamois changing pad covers, one pink and one green, on Ebay. They are both extremely soft and it's nice to have a backup in case of any messes.
Chamois changing pad cover $19 each at Pottery Barn Kids (available in blue, green, pink, yellow, and lavender).