Amanda,
I'm afraid there is no such thing as a death certificate before civil registration began in Scotland in 1855. Prior to this, the best you can hope for as far as the parish register is concerned is a burial record for them. However, it is unlikely to say who the parents were

Having looked at the General Register Office for Scotland's list of old parish registers and the included dates, New Deer parish only seems to have the burials 1690-1700 and 1784-91 recorded. The images are not online at ScotlandsPeople, nor are they indexed.
The only other alternative is to look at the Kirk Sessions records and see if there is any record of the mort cloth rent for either of the burials.
As far as dates of birth are concerned, have you looked for their baptisms on ScotlandsPeople? The exact dates of birth may not be recorded.

Nell