Hi Pergamond,
Although it is vital to consider the possibility of non-conformist records and entries which are missing from the OPRs for other reasons, I believe in this case the OPRs do hold the answer to your puzzle.
I believe the parents of Robert Riddell were Peter/Patrick Riddell (Peter and Patrick are interchangeable forenames in Scottish records of this period) and his wife Betsy/Betty Scott, married on 25 May 1788 at Ancrum. This couple later moved to Oxnam and are buried in Oxnam Churchyard. (Transcriptions are available from the Borders Family History Society:
http://www.bordersfhs.org.uk/BFHSMIAllVolumes.asp)
The only child found in the OPRs where both parents are named is Thomas (b. 19 Nov 1804, Oxnam). However, I believe we can add the following entries where only the father is recorded (although it would be good to check the original OPRs for further confirmatory evidence):
George, bap. 10 May 1789, Ancrum
Robert, bap. 13 May 1791, Ancrum
Margaret, bap. 9 Feb 1794, Ancrum
Peter, bap. 17 Jul 1796, Ancrum
Anne, bap. 12 Apr 1799, Ancrum
Margaret, bap. 11 Apr 1802, Ancrum
Jennet (Janet), bap. 15 Mar 1807, Oxnam
It would appear that Betty was still alive in 1841, when we can see her in the census at Cappuck, Oxnam Parish:
http://www.scottishindexes.com/41transcript.aspx?houseid=79601011She is still alive in 1851, where the census reveals she was born in Hobkirk Parish:
http://www.scottishindexes.com/51transcript.aspx?houseid=80201027I believe Jane Oliver's parents were Adam Oliver and Beatrix (Beatie) Smith, whose marriage is not recorded, but lived in Oxnam Parish. There seems to be the possibility that there was more than one Adam Oliver in Oxnam Parish, but we do have the following children where both parents' names are recorded:
Thomas, born 4 May 1784, Oxnam
Charlotte, born 6 Jun 1785, Oxnam
William, bap. 12 Apr 1787, Oxnam
I believe we can almost certainly add Jean Oliver, father's name Adam Oliver only recorded, bap. 14 Jun 1789 at Oxnam to the above list. Jean and Jane are interchangeable forenames. Hopefully the original OPR will confirm a similar occupation and/or residence for Adam, father of Jean to the other children already mentioned.
The above parents' names for Robert Riddell and his wife Jane Oliver seem to fit well with their children's names listed in an earlier post above. The match of children's names Peter (1818), Beatrix (1822) and George (1828) seem such a good match with later census records that I have little doubt this is your couple.
Hope this helps,
Graham Maxwell