Were medieval priests put in the stocks?

There were doubtless occasions when priests were put in the stocks, but I would imagine they were the exception and this very seldom happened.

Priests were members of clergy. The legal system of the Middle Ages included what was called "benefit of clergy," which provided for clergy to be tried by ecclesiastical courts when they were accused of crimes. Ecclesiastical courts were prohibited from using corporal punishments on several occasions by the popes (a sign it happened from time to time).

Benefit of clergy, by the way, did not only apply to priests, but to all clerics. Today we is envision this as including monks and nuns, but this vision is incomplete. It was rather hard to determine who was a member of the clergy and who was not, so the question was put to a test to determine whether a person qualified, and the test was whether a person was literate to the point of being able to read the 51st Psalm. Under this system, all literate people were clergy, and this included a large number of students, members of nobility, merchants, poets, troubadours, and any scoundrels who had memorized the 51st Psalm.