The 1881 census shows Robert aged 39 and born in Rutherglen. I think his wife is Agnes Ross, and they were married in Rutherglen on 2 June 1865.
The children are John, 1866; Isabella Baird, 1867; David, 1869; Agnes Ross, 1871, Robert, 1873; John and William, twins, 1874.
The Community Contributed (and therefore unreliable) IGI has Robert Tennant, son of John Tennant and Isabella Baird, born in Rutherglen on 1 June 1841.
The 1851 census transcription at
www.freeCEN.org has John Tennant, 42, coal miner, born Barony (i.e. Glasgow) with wife Isabella, 32, born Old Monkland, and Robert, 9; David, 7; William, 5; Agnes, 2; and John, 1; all born in Rutherglen.
The Community Indexed (more reliable) IGI lists two more children, Andrew, born 3 December 1855, and Thomas, 1858. 1855 birth certificates are gold mines of information, so if I were you I would hasten to get that one from Scotland's People.
The 1841 census transcription at FreeCEN has a family in Rutherglen consisting of Robert, 60, coal miner; Jean, 45; Robert, 20, coal miner; William, 15, coal miner; Jean, 25; Elizabeth, 15; John, 30, coal miner; Isobell, 20; Jean, 8; and an unnamed male, aged 6 days. As the census was taken on 7 June 1841, this last is clearly Robert, born 1 June 1841.
These are probably the family of Robert Tennant and Jean Smith. Their son John was born in Barony in 1808.
The only adult John Tennant/Tennent in Avondale in 1841 is a 64-year-old merchant, living at Bank of Scotland.