You might struggle getting back much further that Jeremiah and Ann (although there is a chink of light!).
This is probably their entry on the 1861 census (the surname looks to have been mistranscribed on the index I am looking at):
Jeremiah McRay 35, ship's carpenter, b. Ireland
Ann McRay 30, b. Ireland
John McRay 2, b. Dumbarton
Malcom McDead 46, lodger, b. ireland
Address: 3 xxx, Dumbarton
The children showing for Jeremiah and Ann on IGI:
1. ANN MC KAY Birth: 10 JAN 1855 Rothesay, Bute, Scotland
2. JANE MC KAY Birth: 19 MAR 1857 Dumbarton, Dunbarton, Scotland
3. JOHN MC KAY Birth: 04 APR 1859 Dumbarton, Dunbarton, Scotland
4. JAMES MC KAY Birth: 14 APR 1861 Dumbarton, Dunbarton, Scotland
5. ROBERT MC KAYBirth: 16 JUN 1863 Dumbarton, Dunbarton, Scotland
You have an 1855 birth entry above (by some days!). 1855 was the first year of official registration in Scotland. For one year only the entries ran over two pages of the register and included a wealth of additional info that by 1856 was not given.
For birth certs. it should show the date and place of parents' marriage, where they were from, how many children they had (alive and deceased) etc.
With Irish ancestry, this may be the only chance of finding out where the parents were from. As you can see from the 1861 census entry, most of the time, only Ireland was written up as the place of birth on censuses leaving you with no idea where in Ireland they were from.
I hope you are lucky ~ I would start by looking at Ann's birth cert. on Scotlands People.
Regards.
Monica