The charity has handled 2,500 counselling sessions in the last three years while centres in Glasgow and Aberdeen have dealt with 159 calls on the subject from children in the last year.
"No Going Back" Over Devolving Powers
David Cameron and Ed Miliband have insisted there will no going back on plans to devolve further powers to Scotland despite bitter divisions over future constitutional reform.
First Minister Alex Salmond claimed voters had been tricked into rejecting independence by the joint vow promising a new settlement for Holyrood issued by Mr Cameron, Mr Miliband and Nick Clegg in the days before the referendum.
Mr Salmond, who is stepping down from the job after his independence dream was rejected in the referendum, said the "Westminster gang" were already moving away from the pledge they made.
But the Prime Minister said "new powers over tax, spending and welfare are on their way to Scotland" and the timetable for setting out the plans would be met.
And the Labour leader said: "We're going to deliver. No ifs, no buts, we're going to deliver on that promise."
A Downing Street spokesman said: "The three pro-Union parties have made commitments on further powers for the Scottish Parliament and we have set out a clear timetable to do this.
"Lord Smith of Kelvin has agreed to oversee the process to take forward the devolution commitments with powers over tax, spending and welfare all agreed by November and draft legislation published by January.
"This Government has delivered on devolution and we will do so again in the next parliament."
The Prime Minister has said further devolution meant it was necessary to change the way the Commons worked to ensure that only English MPs can vote on legislation which only impacts on England.
This desire for the new settlement for Holyrood to go hand in hand with efforts to answer the so-called West Lothian question about the rights of Scottish and English MPs has been met with wariness from Labour, which has most of Scotland's 59 seats.
But Downing Street said the two processes would run in parallel, and the timetable for the Scottish reform package did not depend on reaching agreement over English votes for English laws.
A No 10 source said: "That will happen, come what may, no ifs, no buts. It is not conditional on anything."
Mr Cameron said the ability of MPs from the devolved nations to vote on matters which do not affect their constituents was a "basic unfairness" in the constitution.
In the Mail on Sunday he issued a direct challenge to Mr Miliband: "Either resolve this issue with us, or explain to the people of the rest of the UK why they shouldn't have the same powers as we are rightfully devolving to the people of Scotland - why, for instance, Scottish MPs should be able to vote to vary income tax rates in England, when the Scottish Parliament is going to be setting Scottish income tax rates in Scotland."
The cross-party consensus forged between the three Westminster leaders in the effort to preserve the Union has shattered following Mr Cameron's announcement that he was looking at wider constitutional change, which came shortly after Scottish voters rejected independence by 55% to 45%.
Official figures show more than 400 consultant jobs across Scotland are unfilled.
Education Secretary John Swinney will urge rival parties at Holyrood to back his plans for sweeping reforms to Scotland's schools.
Experts described the number as a "real concern''.
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