You are unlikely to find a "Birth Record" as generally prior to 1855, it was Baptisms which were recorded in the Old Parish Records, some of which are available on Scotland's Peiple.
I did a comparison of the quantity of Baptisms recorded and available on SP, from 1840 to 1855; to the quantity of Births recorded from 1855 to 1860.
These Baptisms ran at about 40% of those Births; and it is most unlikely that anyone delayed having children so that the Birth/s would be recorded in thev post-1855 Statutory Records.
Although most Baptisms occurred within a reasonable period after birth, say up to one month, I did see one family where the half-dozen children were baptised en-masse, thus the oldest was about 14 years old at the event.
As you have the Marriage or more likely the Banns leading to a possible marriage, you should try checking directly in the Parish Records concerned; but you would have to locate these.
As the OPRs available on SP are from those parishes which handed over their PRs in 1855 to the newly-established Registrar General of Scotland (not all did this), my suspicions are that William Jr was not baptised or that the baptismal record was lost, destroyed etc in the intervening 90 years.
Another problem is that even where a Baptismal Record does exist, the Most Important Person, the mother, is frequently not even mentioned.
I have checked on SP for other LAING Baptisms in the period 1760 to 1780 on Edinburgh (City)[blank First Names]; 78 show up; and these are reduced to 8 if "WILLIAM" as the father's First Name is added to the Search Parameters.
Zero if William and Mary are used as the parents' names.
You may like to check those 8.
William Laing Bookseller seems to have left a Will available on SP-
No Surname Forename Date Description Type Court Reference 1 LAING WILLIAM 15/12/1832 BOOKSELLER IN EDINBURGH INVENTORY ; TRUST DISPOSITION ; SETTLEMENT EDINBURGH SHERIFF COURT INVENTORIES SC70