could this be their children???  
 
 WILLIAM SHAW  
  Male     (submitted record, not extracted)
 Birth:  29 JUN 1846    
 Christening:  20 JUL 1846   Kilsyth, Stirling, Scotland 
  Father:  WILLIAM BURNS SHAW  
  Mother:  MARGARET BARRIE  
MARGARET SHAW  
  Female     (submitted record, not extracted)
 Birth:  16 APR 1851    
 Christening:  18 MAY 1851   Kilsyth, Stirling, Scotland 
  Father:  WILLIAM BURNS SHAW  
  Mother:  MARGARET BARRIE       
MARGARET SHAW  
  Female     (submitted record, not extracted)
 Birth:  22 DEC 1852    
 Christening:  23 JAN 1853   Kilsyth, Stirling, Scotland 
  Father:  WILLIAM BURNS SHAW  
  Mother:  MARGARET BARRIE     
JOHN BARRIE SHAW  
  Male     (submitted record, not extracted)
 Birth:  26 DEC 1859   Kilsyth, Stirling, Scotland 
  Father:  WILLIAM BURNS SHAW  
  Mother:  MARGARET BARRIE     
DAVID SHAW  
  Male     (extracted record)
 Birth:  01 APR 1865   Kilsyth, Stirling, Scotland 
  Father:  WILLIAM B. SHAW   
  Mother:  MARGARET BARRIE    
and then possibly the son william in 1881.........
   Dwelling:   West Port St
   Census Place:   Kilsyth, Stirling, Scotland
   Source:   FHL Film 0203542     GRO Ref    Volume 483    EnumDist 8    Page 7
   Marr   Age   Sex   Birthplace
Wm. B. SHAW   M   34    M   Kilsyth, Stirling, Scotland
   Rel:   Head
   Occ:   Grocer
Jeanie SHAW   M   29    F   Airdrie, Lanark, Scotland
   Rel:   Wife
   Occ:   Grocer
Maggie SHAW       8 m   F   Kilsyth, Stirling, Scotland
   Rel:   Daur
and just in case it makes a difference, there is another shaw family living next door... (could this be william jr's mother & william sr's wife? - or just wishful thinking?)
   Dwelling:   West Port St
   Census Place:   Kilsyth, Stirling, Scotland
   Source:   FHL Film 0203542     GRO Ref    Volume 483    EnumDist 8    Page 8
   Marr   Age   Sex   Birthplace
W. (Mrs.) SHAW   W   54    F   Kilsyth, Stirling, Scotland
   Rel:   Head
   Occ:   Manufacturer Emp 7 Men 3 Girls
John SHAW   U   21    M   Kilsyth, Stirling, Scotland
   Rel:   Son
   Occ:   Joiner
David SHAW   U   16    M   Kilsyth, Stirling, Scotland
   Rel:   Son
   Occ:   Clerk
Elizabeth BLACK   U   24    F   Kilsyth, Stirling, Scotland
   Rel:   Servant
   Occ:   Servant
hope this is who you are looking for. - there are still plenty gaps in between these childrens ages for there to be other siblings, so i could have missed some 

kind regards, 
Lorna.