Chrissie,
From the IGI (records extracted from the Old Parish Registers):
Parents John DAVIDSON and Martha PAINEBOTH
Thomas DAVIDSON, b 1 Apr bap 19 Apr 1834, Dunoon & Kilmun, Argyll, Scotland
Parents John DAVIDSON and Martha PAINE
Mary DAVIDSON, b 10 Mar bap 8 Apr 1849, D & K
Parents John DAVIDSON and Martha PAYNE
John DAVIDSON, b 1 Dec 1852, bap 24 Nov 1855 D & K
What are the names of Thomas's parents on his death certificate?
Have you looked at the above entries on the film of the D & K OPR? You could order it in to your local LDS Family History Centre. It may not give anything more than the bare facts extracted into the Index - but it is always possible that it might have something more (e.g. the residence or occupation of John snr) which might help. And might show whether PAINEBOTH is a transcription error.
FreeCEN (at
http://freecen.rootsweb.com/ ) has the family in the 1841 census - but under the name DAVISON!
Hillfoot Street, Dunoon & Kilmun
John DAVISON, 30 (remember, ages were rounded down to the nearest 5), Laborer, born Ireland
Martha DAVISON, 30, b Ireland
Thomas DAVISON, 7, b Argyllshire
Martha DAVISON, 2, b Argyllshire
John DAVISON, 2m, b Argyllshire
Donald MCQUEEN, 30, Police Officer, born Scotland but not in Argyllshire
Walter MCPARLAN, 25, Flesher, born Scotland but not in Argyllshire
Presumably the John who was 2m old in 1841 must have died as the name was re-used for John b 1852.
Remember that Statutory Registration did not start in Scotland until 1855. And many marriages and baptisms before this were not recorded, or the records have not survived, or the records have not been transcribed.
You could search for the deaths of John snr and Martha snr on ScotlandsPeople as it is quite likely that they survived until 1855 or later - death certificates normally show the names of parents. You can search using wildcards e.g. Martha DAVI*SON. Deaths of married women were also indexed under their maiden names, if known. So you could also search for Martha PA*NE*. If you find an entry for each name with the same reference number, you will know you probably have the right person
You could also order the films of the 1851 and 1861 D & K censuses in to your local LDS FHC - the family was still there when the second John jnr was b in 1852 and bap in 1855.
Regards,
Judy