Thanks for your comments. Because it is/was a troop bylaw, I will have my son meet with another counselor that I will find through council.
While looking through the link that OakTree sent, from the Boy Scouts National Council, I did find in the Frequently Asked Questions:
Question: Can merit badge counselors coach their own sons or close relatives (for instance, a nephew)?
Answer: Yes, but only if the young man is part of a group of Scouts who are all working on the same merit badge. Approved counselors may coach any Boy Scout who contacts them through the proper procedures.