If I were searching on FreeBMD, which of course does not cover Scotland, I would enter the family Surname and the mother's maiden name and an appropriate period and the database would return a list of children matching the criteria.
On SP there seems to be no provision for searching against the parents' names, and entering the child's name, even assuming that it is a correct first name, delivers a list of several dozen. There is then no way to view the entries to see which may be the right one . The only option offered appears to be to order all the certificates, at substantial cost, with no guarantee that any will be relevant.
This is because of the cut-off dates for the
online system. You are not permitted to access
online any details of any birth less than 100 years ago other than the name, year, district and reference number.
There is a way round this, which is to go, or to get someone to go on your behalf, to the Scotland's People Centre.
In-house, you can search for birth registrations from 1929 onwards using the mother's maiden surname, and you can view and transcribe the information on the certificates, but not download, save or print the document. There is a charge of £15 per day for a day's use of the SP centre, but if someone is going there anyway, they should be able to transcribe all the details of quite a large family in half an hour or so.
Using FreeBMD, there is no way to view original documents of a similar vintage at all, either online or in-house. You have to buy every individual certificate at £9.25 each. If you order more than one recent certificate at a time from SP they cost £10 each.