As you can probably guess - there is no possibility of you being able to fine a Council for this.
I practice in government law and see people trying to do things like this very often. Some claims can be quite entertaining, so I'm not discouraging you from trying to do this (just don't get your hopes up if you do try!).
People often neglect much easier routes for complaining about "over-zealous" traffic officers (if that's what you're complaining about). Complaining to your divisional Councillor, presenting local ratepayer petitions for consideration at Council meetings or contacting the Ombudsman (if things are really bad) are likely to be much more productive uses of your time.
That said, if you're parking illegally then any such action will likely fall on deaf ears.
I do note though that if you're complaining about Council's ability to restrict parking in a certain area then consideration would need to be given to the traffic legislation that applies in your area, including your local Council's by-laws. You could raise such concerns in the traffic law forum - you'd just need to provide details of the relevant "restricted parking area" and the council area in which you live.
Hope that helps.