In essence, care should be taken lest the Sacrament of Confession be confused with psychological counseling. A priest with a degree in psychology should be sure not to confuse the spiritual purpose of the Sacrament with the therapeutic purpose of psychology.
Therefore, the proper procedure would be for the priest to instruct the penitent to bring up his psychological issues outside of Confession. In Confession, what is dealt with is sin and grace (see Catechism of the Catholic Church [CCC] 1422); psychological counseling regards the cognitive and emotive faculties.
Naturally, if the priest is acting in the capacity of a licensed professional psychologist (outside of Confession, obviously), then he may seek remuneration like any other. He may not, of course, charge for Confession. (See CCC 2121.)
(I do not believe there is any official legislation regarding this issue, but I suggest reading the overview on the Sacrament of Penance in CCC 1422-1470; you will see that psychological therapy does not really belong to it.)
Aside from the theological issues, confusing Confession and counseling poses practical issues: for example, a priest can never divulge anything he has learned in Confession for any reason. (See Code of Canon Law, 983.) Hence, for example, it would be complicated for him (if not impossible) to consult other psychologists, or refer the “patient” to other psychologists.
The proper procedure, then, would be to counsel the penitent to seek psychological counseling (should that be advisable). If the priest is himself a licensed psychologist, he could even suggest that the penitent seek his help outside of confession.
(I think that most priests in this situation, however, would advise the penitent to go to a different therapist or counselor, since it can be complicated to keep track of what has been said under the seal of Confession and what has not.)