The database is actually terrific and is searchable here:
http://www.scotlandspeople.gov.uk/You have to register (free) and you can do searches without paying but will only be told whether there are matching results. To see the results found you have to buy credits. It's really cheap. Then if you want to see the original image of the record you've found, you pay more credits and access it right on line.
Old parish records are:
» Births & Baptisms 1538-1854
» Banns & Marriages 1538-1854
» Deaths & Burials 1538-1854
Obviously they aren't complete, and you have some pretty common names, and don't know a location. So you will have a hard row to hoe. I'm not sure of your timeline, but if you do have a child born in Scotland and know an approx date and/or a parent's name, you would have a starting point.
I've only ever needed two Scottish records personally - a grx3 grandfather from England turned up, bizarrely, in the 1841 Scottish census. I hadn't even thought to look for him there -- I had him in the 1851 and 1861 before he died, have his and his siblings' baptisms and his parents' 1782 marriage from parish records, all in the same place in England. No idea why he was in Scotland and wouldn't have looked, but someone at the genealogy board where I was talking about being unable to find his marriage and his son's birth came up with a (second, presumably) marriage in Scotland that was beyond question him, from the name. Then shortly after came his wife's death. Apparently I was very fortunate at all the detail in the records -- parents' names, occupations, ages, etc. The pre-1855 parish records tend to have sparse info.
I'm in touch with someone who works for the Scottish registry office and has access to all these old records. If you come up with something and need help sorting it out, drop me a PM.
typos fixed