On Tuesday the group won support for their concerns from MSPs on the Scottish Parliament's petitions committee.
Now they are to lobby officials in the Scottish Executive's health department over what they allege are the drugs "alarming side effects".
The parents said that there are better non-drug treatments available for children who suffer from hyperactivity or attention deficit disorder (ADD).
Ritalin was approved for prescription on the NHS to treat ADD two years ago.
The symptoms of ADD range from poor concentration and extreme hyperactivity to interrupting and intruding on other people.
Ritalin is a mild stimulant - an amphetamine - that works on the central nervous system to improve concentration.
The drug is manufactured by multi-national pharmaceutical firm Novartis.
Serious concerns about its effect on children were raised by the Scottish Association for Mental Health last year.
The charity called for a review of the drug and said its long-term effect on children was unknown.
Mood changes
Now Scottish parents, led by James Mackie from Alloa, want alternative treatments to be offered on the NHS.
Representatives from the protest group said their children had suffered side effects such as loss of appetite, stomach pain, increased blood pressure and skin rashes.
They also said that their children's moods were subject to change and in some cases they suffered from delusions.
On Tuesday, the parent's group won the support of the Scottish Parliament's petitions committee for a review of the use of Ritalin and another neuroleptic drug Clozapine, sometimes used to treat autism.
They argued that psychiatrists were using such drugs as "chemical lobotomies" instead of experimenting with other treatments such as exercise or diet changes.