"Chance favors the prepared mind." - L. Pasteur
While you can't choose your own appraiser, you CAN be prepared for when the appraiser shows up.
Suggestions:
Meet the appraiser at the property to allow for access.
Hand him/her a copy of your best comps. If you don't have them, get them from your realtor.
Include a list of specific value-added upgrades that might possibly be overlooked. (New A/C, kitchen renovation, bath upgrades, etc.)
Don't assume that the appraiser knows more than just the raw numbers of the neighborhood. Be prepared to clarify low-value closed comparables that an appraiser might not be aware of (ex: "Yes, that property was on the market for a long time and sold at that price because there was a murder-suicide in the home.")
Make sure the property is in the best "showtime" condition (no dirty dishes in sink, no laundry on the couch, quiet, and clean).
With this said, the appraiser does not HAVE TO accept anything you provide and may carry on doing the work without any of your input. He/she may still find a value significantly lower than you expect. At that point you can appeal the value and call out any factual errors, with a low likelihood of success, but still a possibility. If that fails, you can opt to pay for another appraisal, and start anew with another lender.
Hope this helps,
-IrvineRealtor