Golspie,
The Day Book records only begins at 1876 and only has a few entries for that year. It doesn't get going until the end of 1877 and I can't find anything for Charles and Ann, sorry.
There was a private burial ground too, and there are some burials for the children of Alexander Richardson and Janet Cowan. Do you recognise these names? Could Alex and Charles have been brothers?
Childrens details -
HUGH RICHARDSON, Wishaw, aged 2 years.
Interred plot No. 161, 1st January 1876.
JANET RICHARDSON, Wishaw, aged 9 months.
Interred plot 161, 26th May 1879.
THOMAS C RICHARDSON, Wishaw, aged 11 years.
Interred plot 161, 27th August 1891.
Also -
HELEN RICHARDSON, servant, Waterloo, aged 21 years. Single.
Parents Charles Richardson and Jane Archibald.
Interred plot 188, 2nd February 1871.
Also the following, there may have been a transcription error as the grave is No.188 as before.
CHARLES R ROBERTSON, Wishaw, aged 17 months.
Parents Charles Robertson and Jane Richardson.
Interred plot 188, 6th April 1872.
I think the mother may have been Robertson and the father Richardson.
That's the best I can do. good luck with the research, keep posting querries on Rootschat, it's always worth a try.