I did some looking in Newport, RI for Moloney and variants. I thought the first man listed here was the most interesting possibility.
----
1830 Census of Newport, Rhode Island
page 33. [image 63 at ancestry.com]
Sanders Mullone/Mullane
household: 1 white male 70 to 80
https://www.familysearch.org/ark:/61903/1:1:XHP4-92HI don't see him in 1820 in Newport. the 1820 census of Newport was recorded alphabetically by surname.
-----
1840 Census of Newport, Rhode Island
all white:
John Melloney (b 1800 to 1810 - )
+ __ (b 1800 to 1810 - )
- female (b 1830-1835 - )
- male (b 1835-1840 - )
- female (b 1835-1840 - )
Patrick Melloney (b 1800 to 1810 - )
+ __ (b 1800 to 1810 - )
- female (b 1830-1835 - )
- male (b 1835-1840 - )
https://www.familysearch.org/ark:/61903/1:1:XHYB-8FN-----------
death of an Ann Mulooney indexed on familysearch, with some added information from ancestry.
(c 8 Aug 1857 - 8 Feb 1857, Newport), father: John Mulooney, "kin 2: Wm Springer" -
https://www.familysearch.org/ark:/61903/1:1:QL92-TBLFshe could be a daughter of John Melloney on the 1840 census.
---------
This lady could be the widow of John or Patrick. found this on ancestry.com
1865 Rhode Island Census, Newport, Ward 5, family 2137 - all one household
Maloney
Ann, 65, born in Ireland, cannot read or write, housekeeper
Murry,
Ann, 22,
John, 15
Mary A, 12
Ambrose, 10
Sarah, 5
Dorcas, 4
All the Murrys were born in Newport
----------
1863 Newport Directory
Patrick Maloney, laborer, home at 55 Thames
Timothy Maloney, grocer at 9 Tanner, home at same address
There weren't any Maloney variants in the 1856 Newport directory, and that is the earliest one at ancestry. I haven' looked elsewhere yet.
----------
and for New Bedford, Massachusetts:
1820 Census - I didn't find any Moloneys in New Bedford, Massachusetts. the names are listed alphabetically.
on the 1830 Census of New Bedford the names are not listed alphabetically. there are 102 pages. I didn't go through them. you could browse them at familysearch if you want.