Summaries of research reports that suggest that absolute pitch ability can be learned and improved through practice (note that "perfect pitch" is usually called by researchers "absolute pitch"):
Lola L. Cuddy
"The experiments reported in this paper suggest that learning or past experience plays an important role in determining the ability to judge musical pitches. Experiments 2 and 3 indicate that pitch judgment can be improved through a specific kind of training on the identification of a single tone."
"Practice Effects in the Absolute Judgment of Pitch," by Lola L. Cuddy, in The Journal of the Acoustical Society of America 1968, Vol. 43, 1069-1076.
Note: Cuddy's most successful training method is similar to that described by Paul T. Brady. Cuddy uses the note A instead of C and simply requires subjects to identify a note as "A" or "Not A". This type of training can easily be implemented with EarTest.
EarTest is a Windows program that allows you to practice perfect pitch (and relative pitch) ear training. EarTest is flexible--you can try all the practice methods suggested by these studies.