Taking minutes is not my strong suit. Should I be required to take minutes at my supervisor's board meetings?

I think the fact that it isn't your strong suit is exactly the reason you should do it. Minutes are easy. You just need to know what your boss considers to be important and ask him in advance for direction. Think of minutes as a summary of a meeting. Just outline what was discussed. Passing tasks to other people that you are not comfortable with, will not help you grow and will limit your promotion/raise opportunities.

Actually, I think it would be one of your duties. I wasn't that good at it either and really wasn't supposed to be doing that kind of stuff. I worked for the Public Service Dept. for our city but I was injured and had to work at city hall for a few months. The lady I was replacing had to take a leave of absence for her hubby's chemo treatments. It was hard but you will get used to it. My advice if you city has city commission meetings go to their secretary/receptionist and ask for a copy of their templates for minutes of the board meetings. I am sure they will be more than happy to oblige. It makes it easier. Also instead of trying to write down all that were present at the meeting have a sign in sheet at the front door so they can write it down for you. Most templates for board meetings are typed out with the agenda/decisions that need to be made a box that you check for either passed or declined and then you write in who made the motion and who seconded it and who agreed. This template would be a lot easier than you just writing everything down.

I agree with David, it would not be wise to pass up this opportunity to show your boss that you can learn to do things you're not really good at.

Good Luck.