When I do a search of the 1830 US Census no entries for Carteret County, North Carolina are returned. The "Browse this collection" drop-down does not offer Carteret as a county in North Carolina.
A search of the 1840 US Census also does not include any entries for Carteret County, North Carolina, but Carteret County is an option on the "Browse this collection" drop-down for this year. When I use the "Browse this collection" drop-downs set to North Carolina and Carteret County with no other criteria no records are returned (Your Search returned zero good matches.)
Is this an Ancestry database problem or are there no records for Carteret for these years?