We know a daughter married a Harrison from David's will.
A single Harrison in Franklin Co, TN 1830 named "John Harrison" with family, however in land deed of 1817, David Robinson sold to "Daniel Harrison" -
http://groups.yahoo.com/group/emerson_robinson/message/479
Daniel Harrison in Franklin Co, TN 1820 (on ancestry.com - believe this is Franklin Co part of census, not Jackson Co)
Enumeration Date: August 7, 1820
Free White Persons - Males - Under 10: 3
Free White Persons - Males - 10 thru 15: 3
Free White Persons - Males - 16 thru 25: 1
Free White Persons - Males - 45 and over: 1
Free White Persons - Females - Under 10: 1
Free White Persons - Females - 16 thru 25: 2
Free White Persons - Females - 26 thru 44: 1
Appears to be them in 1830 Lincoln Co, TN:
Free White Persons - Males - 5 thru 9: 1
Free White Persons - Males - 10 thru 14: 1
Free White Persons - Males - 15 thru 19: 1
Free White Persons - Males - 40 thru 49: 1
Free White Persons - Females - 5 thru 9: 1
Free White Persons - Females - 15 thru 19: 1
Free White Persons - Females - 20 thru 29: 1
Free White Persons - Females - 40 thru 49: 1
Next to the Robinson's in Franklin Co, TN 1850 is David Harrison hh. David b.1815 prob their son.