With the education Bill now going through line-by-line scrutiny in the Scottish Parliament, councils want to outlaw those who buck the system by giving fraudulant information. They say a minority of parents resort to all sorts of dodges to evade catchment area regulations.
Some give false details about renting or leasing houses, forge solicitors' letters, disguise business addresses as private residences or give relatives' addresses, and even pretend a marriage has broken up. Others have reported a child moving in with an estranged parent before moving back home.
Mr McCafferty said parents should be penalised and there could be circumstances where the child could be withdrawn from a particular school. But he added: "The child should never be penalised for the parents' sins."
The Convention of Scottish Local Authorities wants ministers to reconsider the entire placing request legislation, which so far they have rejected. Existing legislation runs to around 20 pages, spread over five different Acts over the past 20 years, according to David Henderson, head of policy and development.
"It's hugely complex and we want to simplify it so that it's easier for everyone to understand," Mr Henderson said. Because of the confusion sheriffs tended to make different interpretations of the law.
Local authorities, Cosla suggests, should have a duty to develop local schemes for admissions to schools within agreed national principles and criteria
Each primary and secondary school would have a standard number of pupils representing its cpacity set centrally and approved by the Scottish Executive. A number of places could then be kept in reserve for pupils moving into the catchment area. Each authority would publicly announce the numbers of pupils at each stage. Numbers could not be exceeded.
Among other amendments, Cosla proposes allowing access to two full years of nursery education if families want it, easing the financial predicament of parents and local authorities.
Currently councils do not receive Government funding for a nursery place if parents opt to delay their child's entry into the first year of primary.
Some children also lose at least a term of nursery entitlement because of the date their birthday falls on. With rising concern about the educational disadvantages of pushing younger children into P1, authorities believe they have the support of parents.
A further amendment seeks to ensure school boards become a vehicle for wider parental involvement and not the prime focus of all parent activity.
Mr McCafferty said boards had developed differently from the intention of the Conservative administration in the late 1980s and legislation now needed to catch up.
"Parents joined school boards to defend schools from being hived off. What we are saying is perhaps we should now rethink and put forward within school board legislation more clear statements of what their role should be. It is not just to meet every so often to consider reports from headteachers but to actively support the school and participation of parents," Mr McCafferty said.
He accepted ministers had rejected a wider review of boards, the chief reason why Cosla was proposing a more modest amendment about a duty on boards to widen participation.