There is a Gilbert Laird Baptism or Birth recorded on Scotland's People, Old Parish Registers, 31st July 1796.
Mother's name is Elizabeth.
If you purchase 30 Credits costing UK£7 ( about US$12), you can access the Scanned IMAGE of the Register (OPR), using 1 Credit to access the Search INDEX brief informations; and 5 Credits to VIEW the IMAGE including downloading it to your PC.
A Credit or Debit Card is the quickest way of doing so, giving you access within seconds.
That Image may or may NOT have more information, the contents of the OPRs generally are quite brief.
In fact, I was surpised to find the mother's name, as generally these are not included!!
This is the only record that is a near-match to your information.
Incidentally, it is helpful if you include the sources of your information.
If he lived in Belfast from 1832 to 1851/1852, you would have to locate the 1841 and 1851 Irish Censuses to make progress.
Noting the chlidren in this 1860 USA Census are born in Ireland, I wonder if there is any confusion-
Name: Gilbert D Laird Event Type: Census Event Year: 1860 Event Place: 3rd Ward Providence City, Providence, Rhode Island, United States Gender: Male Age: 65 Race: White Race (Original): [Blank] Birth Year (Estimated): 1795 Birthplace: England Page: 4 Household ID: 28 Affiliate Name: The U.S. National Archives and Records Administration (NARA) Affiliate Publication Number: M653 GS Film Number: 805208 Digital Folder Number: 004293576 Image Number: 00008 Household Gender Age Birthplace Gilbert D Laird M 65 England Harriet Laird F 51 England Thomas H Laird M 31 Ireland Robert Laird M 20 Ireland William Laird M 12 Ireland
There these entries on Castle Garden, predecessor of Ellis Island-
LAIRD JOHN 23 M 18 May 1850 U LAIRD MARGARET 21 F 21 May 1850 U LAIRD SARAH 22 F 19 Sep 1850 U LAIRD THOMAS 21 M 19 Sep 1850 U LAIRD HUGH 6 M 27 Sep 1850 U LAIRD JAMES 29 M 27 Sep 1850 U LAIRD GILBERT 0 m M 30 Apr 1851 U LAIRD HARRIET 20 F 30 Apr 1851 U LAIRD MARY-A. 12 F 30 Apr 1851 U LAIRD ROBT. 10 M 30 Apr 1851 U LAIRD WM. 5 M 30 Apr 1851 U LAIRD JNO. 22 M 16 May 1851 U LAIRD MARY 20 F 4 Nov 1851 U LAIRD ELIZA 16 F 13 Nov 1851 U LAIRD MARY 18 F 13 Nov 1851 U LAIRD ELLEN 8 F 7 Jul 1851 LAIRD ESTER 30 M 7 Jul 1851 LAIRD JESSEY 20 M 13 Dec 1851 U LAIRD JOHN 30 M 2 Oct 1850 U LAIRD NANCY 20 F 10 Dec 1850 U
The Scottish Records are held in New Register House in Edinburgh, directly opposite the Balmoral Hotel at the Eat end of Princes Street. (The clock is kept two minutes fast, to help people get down to the Waverley Station on-time, to catch their trains.)
There is a large statue in front on the wide side-walk, "The Iron Duke, on his Horse of Bronze, On a Granite Plinth, all by Stiell".
Also keep your ears open (or covered) when the "One o' Clock" is fired from The Castle.
All of the BMD etc Records are available on-line via Scotland's People, so you are unlikely to make any more progress there; but I do think you should take the opportunity to visit, particularly The Dome where the originals are kept. Follow the cafe signs to get there.