The report, due to be finalised in May, states that based on previous research estimates a fifth of children and young people have psychological problems that would benefit. Parents are pressing for help with problems associated with developmental delay or mental health.
Increased recognition has also been given to the psychological impact of chronic conditions such as asthma and diabetes.
The two bodies drawing up the report - Clinical and Applied Psychologists in Scottish Health Services and the Scottish Council for Postgraduate Medical and Dental Education - say that with resources static the shortfall in Health Service provision means waiting lists of up to a year in some parts of the country.
The situation was described by Pat Dawson, director of the Scottish Association of Health Councils, as "atrocious".
Alan James, clinical child psychologist with Ayrshire and Arran Health Care NHS Trust and head of a psychologists' working party on services to children and their families, says: "It is frustrating for parents as they don't see their children's needs being met as quickly as they want."
Mr James warns that where children in schools or nurseries are left to flounder with "attentional and behavioural problems" there is "bound to be an impact".
There are fewer than 60 full-time equivalent NHS posts for clinical psychologists working with children and families in Scotland. Young people can also be seen by one of 340 educational psychologists employed by councils.
"There is a gap between demand and supply and a shortfall in expert psychological advice in schools," Brian Kirkaldy, Fife's principal psychologist and chair of the Association of Scottish Principal Education Psychologists, says.
The association has persuaded the Scottish Office to approve an extra 10 training places for educational psychologists on top of the current 24. But 14 local authority posts are unfilled and provision varies widely among local authorities, Mr Kirkaldy says.
The number of training places for clinical psychologists has risen to 32, but only from what Graham Buckley, executive director of the postgraduate council, describes as a "very small base".
Mr Kirkaldy says that the type of psychologist a child is initially referred to is often "a matter of chance". If a child "with significant unhappiness" is left on a long waiting list "this will have an impact on the school and on us", he warned.
Gwynedd Lloyd, senior lecturer in equity studies and special education at Moray House Institute, says that demand on child psychology services has risen partly because of publicity for conditions such as attention deficit disorder. The target-oriented school system also puts "children under more pressure to perform, and teachers are less able to be tolerant".
But she adds: "The answer may not necessarily be to have lots more psychologists. School-based resources are important too."