Hi lynnd08 and welcome to Rootschat.
There is a Walter Beveridge on the 1851 Scottish Census in Dunfermline, Fife.
His address is given as Halbeath Colliery,
Walter Beveridge   M     Head         27            Coal Miner          Fife Dunfermline
Catharine Beveridge   F  Wife          42           Wife                      ditto
James Beveridge      M    Son            7           Scholar               Fife, Dalgety
Robert Beveridge     M    Son            6           Scholar               Lanarkshire, Monkland
Betsy Beveridge       F    Dau             3                                          ditto
This looks like the couple you are researching although Catharine/Catherine's age is older than your info indicated . Of course this could be a mistranscription. I copied the info from Freecen's website.
The area around Monkland in Lanarkshire where the younger children were born was also a major mining area so Walter must have worked there too.
Looby 
