Yes your ancestors were Manx, if this was the correct Robert, which looks likely (because of the June birth month recorded in the USA). As previously mentioned there were a lot of Robert Corkills in the IOM, and many blacksmiths in the Corkill families.

You need to follow the census records to establish Robert's father Robert's age, and then look at parish registers on LDS film to go back further. His wife Cath QUAYLE is recorded in 1861 as born Bride c.1819, but sometimes census data varies, so you need to check them all. Robert is recorded as b.c.1820 Maughold in the 1861 census, which, if correct, makes him very young at his marriage on 3 Aug 1839. There are three Robert Corkills bapt in Maughold between the second half of 1819 and 1821.

I have only the 1841 Maughold census (1881 is online at FamilySearch.com).

1841 census (adult ages rounded, relationships not given):
1 4 14 East Ballaterson Thomas QUAYLE 30 MS Isle of Man
1 4 14 East Ballaterson John GARRETT 25 MS Isle of Man
1 4 14 East Ballaterson Robert CORKILL 20 Blacksmith Isle of Man
1 4 14 East Ballaterson Cathrine CORKILL 20 Isle of Man
1 4 14 East Ballaterson Jane CORKILL 1 Isle of Man
1 4 14 East Ballaterson William KINRADE 6 Isle of Man.

1881 census:
Robert CORKILL Head M Male 60 Maughold, Isle of Man Blacksmith
Catherine CORKILL Wife M Female 60 Bride, Isle of Man Blacksmith's Wife
Source Information: Dwelling 2 College St
Maughold, Isle of Man
Family History Library Film 1342345
Public Records Office Reference RG11
Piece / Folio 5600 / 98
Page Number 14

Two possible Robert Cs b.c.1820 were bapt in Maughold 29 Aug 1819 (son of Robert Corkill & Esther Looney), and 11 June 1820 (son of Peter Corkill & Elinor Clague).

The first one fits his age in the 1861 and 1881 censuses, and 'Esther' and 'Robert' names were used for children - but so was Elinor later.

Other census records and wills might help.

Sue