Something to chew on  

RICHARD COLE 
  SARAH PINK  
  Marriage:  27 NOV 1738   West Worldham, Hampshire, England 
Either Stephen an 
 unreadable baptisem  at Binsted or as below West Worldham 
Assuming Steven was there first born say West World ham
the first Baptism Binsted for Richard was JOHN COLE  Christening: 13 MAY 1743 Binsted Near Alton, Hampshire, England 
 next HANNAH COLE Christening:  18 OCT 1745   Binsted Near Alton, Hampshire, England 
 next THOMAS COLE Christening: 26 DEC 1747 Binsted Near Alton, Hampshire, England
There were 3 marriages around 1760's for Stephens one at Ringwood 1766 and there is a Stephen birth/bapt for him about 1740+/-
and one marriage marriage  at Romsey 
one at Binsted and the Stoke Charity Stephen bapt 1737 could be either marriage
Last there is a bapt fro a Richard father Thomas in Binsted 1757 but seems late for this Thomas to be Stephens father