Scott Cochrane has some great advice for you on how NOT to deal with the complainers in your church:
1. Don’t take on every complaint yourself
A common mistake made by inexperienced leaders is to assume that simply because someone brought a complaint to your attention, that it now becomes your problem to solve.
2. Don’t get defensive
Effective leaders know that even within the shrillest sounding complaint, there can be a kernel of truth worth listening to.
3. Don’t miss out on a teaching moment
When a complaint comes forward, even one laced with sarcasm and hurtful language, you have an opportunity and responsibility to coach and correct.
Good advice… You can read more from Scott here.
How do YOU deal with complainers in YOUR church?
Todd

Also, figure out what kind of complainer (whiner) they are. Are they just complaining because they like to complain? Do they have a legitimate beef even if I don’t want to hear it? Do they feel ineffective and just need help coming up with a solution so that they can move forward?
I’ve found too that whiners / complainers are often targeted by church bullies, who want to control the ministry. If you don’t take care of the complainer, they can become an even bigger pain if they tag team with the bully.
Just my two cents!
I use a “somebody list.” This is when the complainer asks for something not high on the priority list. Usually it is a ministry they want but few others would value. I tell them i’ll put it on the “somebody list.” That’s the list of things that will get done when somebody steps up to lead in that area. If they have the right gifting I will ask if they want to solve that problem. It validates the need/ desire while not-so-subtly communicating that fixing the issue is not my priority. Sometimes it motivates them to solve their own problem and usually it ends the conversation. Many items on the list do get done…eventually.
I would add – Don’t deal with complainers at the worship service (before or after). Their attitude and words can hinder your attention and proper attitude. Give them an ear at a more appropriate time during the week. This may also weed out those that don’t want to take time out of their week. I also have them come to my office instead of going to them. If they have something that is truly important to them, they will make the effort. Don’t deal with complainers via mail or email or over the phone. Make them tell you face-to-face. This often reveals any weaknesses to their point or calms them down when they have to look you in the eye and answer your questions as they explain their point.