Thanks, Dan, for the message. Since I first posted my message I have discovered a lot about Robert Monroe Harrison's career and family. I am reliably informed that his father was Robert Hanson Harrison and his mother Sarah Johnstone. However we have not yet been able to obtain confirmation by church record of his birth, details of which are on his gravestone in Jamaica.Also we still have not found any church record of his marriage to Margaret, but various factors lead us to believe that they married in Sweden.
On the assumption that his father was Robert Hanson Harrison, I have traced details of his line right back to England. I too once wondered if the name Monroe was the maiden name of RMH's mother. However, having seen the close connections his father had with Presidents Washington and Monroe and the fact that the family of RMH's cousin President William Henry Harrison had a long connection with Monroe, Ohio, I guess that RHH gave his son RMH the additional name Monroe for these reasons. Also, RMH named one son after William Henry Harrison and gave two other sons the second names Washington and Adams, as he RMH had in his career as Consul to Jamaica been close to the two Presidents. So giving Presidential names seems to have been quite an obsessionin the family.
Many thanks again for your interest - if you do come across details one day of his birth or marriage, I'll be ever indebted to hear from you.