I have a paper on US Naval Construction, essentially (largely copy and paste, the dates are those of authorisation. Any implication of completion dates should be avoided, 10 years after the 1816 act, not all of them had been laid down, at 2 of the 10 1816 frigates weren't finished in 1853. None of the Sail of the Line were ever finished as warships).
1816 act: Sail of the Line Alabama, Columbus, Delaware, New York, North Carolina, Ohio, Pennsylvania, Vermont, and Virginia; and frigates Brandywine, Columbia, Cumberland, Potomac, Raritan, Sabine, St. Lawrence, Santee, and Savannah. (see 1826 for the 10th frigate)
1820 act: schooners Alligator, Dolphin, Grampus, Porpoise, and Shark
1822 act: steam gallion Sea Gull, schooners Beagle, Fox, Greyhound, Ferrett, Jackell, Terrier, Weazel, and Wildcat, and barges Mosquito, Gallinipper, Gnat, Midge, and Sandfly
1825: All ships on the Great Lakes except New Orleans and Chippewa (both on the stocks) are disposed of, Boston, Concord, Fairfield, Falmouth, Lexington, Natchez, St. Louis, Vandalia, Vincennes and Warren acquired. Sloops John Adarns and Peacock rebuilt
1826: Authorises the purchase rather than construction of 1 of the 10 1816 act frigates (as a private construction's buyer had fallen through), becoming the Hudson.
1830: schooners Enterprise, Experiment, and Boxer authorised
1831: money to reconstruct frigates Java and Macedonian and sloop Cyane
authorised. The request to build 2 steam gunboats rejected
1834: request for timber for a new frigate, to be called Paul Jones, and a new sloop-of-war, Levant, along with authority to purchase or build two shore-ships. The act of June 30, 1834, authorized procuring of timber for the frigate, and sloop, and the building of a store-ship and two small
vessels. Small brigs Dolphin and Porpoise and store-ship Relief resulted from this act, but Paul Jones was never built and Levant authorized later. A second act of June 30 authorized rebuilding of frigate Congress.
1836: authorization for the President to purchase small vessels for the proposed South Seas Exploring Expedition. Brigs Pioneer and Consort and schooner Pilot were built for the expedition but found unsatisfactory and replaced by purchased schooners Flying Fish and Sea Gull.
1837: The Act of April 3, 1837, authorized building of sloops Cyane and Levant using frames already provided as well as six additional ten to eighteen gun warships. The latter became the five Dale class brigs and
screw sloop Princeton. The latter became famous as [America's] first screw man-of-war.
1839: The Naval Appropriation Act of March 3, 1839, authorized three steam warships "on such models as shall be most approved." The impetus for this act is obscure but it seems to have come from outside the Navy Department since the 1838 Annual Report contains no such request. The three vessels were Mississippi, Missouri, and Union. The next act, March 3, 1841, provided for three medium size steamers. Only one was completed,
Southnmpton, and she came out as a sailing storship. September 9 of that year Congress appropriated $100,000 for the construction of Great Lakes steamers." Only one was built, the iron hulled gunboat Michigan.
1842: Steven's Battery authorised
1844: authorisation of Alleghany built at Pittsburgh to test further Lieutenant William W. Hunter's idea of horizontal paddle wheels.
1846: On May 11, 1846, the United States took possession of the remnants of the Texas Navy, a sloop-of-war, two brigs, and a schooner. Inspection showed none worth repairing and all were sold although sloop-of-war
Austin lasted until 1848 as the Pensacola receiving ship. Hunter, Iris, Scorpion, Scourge, Spitfire, and Vixen; bomb brigs Etna, Hecla, Stromboli,
and Vesuvius; schooners Bonito, Petrel, and Reefer; and store-ships Electra, Fredonia, and Supply added by purchase.
1847: Secretary Mason included a recommendation for four steamers in his December 5, 1846, Annual Report and Congress concurred in the Act of March 3, 1847. The four were the highly successful and useful Powhatan,
Sun Jacinto, Saranac, and Susquehanna.
1849: Two years later the Naval Appropriation Act of March 3, 1849, transferred to the Navy all the surplus and unwanted Army steamers left over from the war. Only two, Massachusetts and Edith, were kept; the
others were either sold or returned to the War Department.
1853: In 1853, the Navy purchased the small steamer John P. Kennedy and schooner Fenimore Cooper for use by the Ringgold North Pacific Exploring Expedition. The appropriation covering their purchase was contained in the Naval Appropriation Act of August 31, 1852.
In his 1853 Annual Report Secretary James C. Dobbin added his voice to the call for an enlarged navy. He stressed the lack of large steamers and the poor condition of many of the older vessels. Dobbin recommended construction of six screw frigates and conversion of Franklin to a seventh. Congress responded with the Act of April 1854, authorizing the six screw frigates and completion of the last two 1816 sailing frigates, Sabine and Santee. These screw frigates were Colorado, Merrimack, Minnesota, Niagara, and Wabash. The sixth, Niagara, was built as an oversized screw sloop.
So, one half decent steamer (Princeton), some coastal ships and a lot of dubious 1810's era sailing ships....