The best source for that information would be the baptismal records. You can call the mission and see if they have a copy.
Most of the original records for all the missions are maintained at:
Santa Barbara Mission Archive Library 2201 Laguna Street Old Mission Santa Barbara, CA 93105. Telephone: (805) 682-4713.
Since you are only searching for one or two names you may find someone who is willing to give you that information over the phone.