The 1830 census tallies a girl in the 5-9 age bracket, and so probably born before Ephraim. And two boys under age 5, could mean Joseph was born just prior to the census. [3116]

The same 1840 census page also lists a Lyman WHEELER, which is the name of Ephraim SMITH’s father-in-law, thus enhancing the likelihood that this is the correct Oliver SMITH. [3106]

Possibly married “Nancy A.” after death of Deborah? (see Find A Grave Memorial# 19869948)

An Oliver SMITH, born 19-JUN-1800, in West Haven, Rutland Co., Vermont, may be this person. The record states that his father’s name was Joseph SMITH. [3109] On Familysearch.org, this record is part of Batch 7450237, which includes the following additional children attributed to Joseph SMITH in the same place and time period: Sarah SMITH 15 Jan 1794; Polly SMITH 07 Aug 1808. Ancestry.com’s Vermont Vital Records includes those index cards as well as ones for Israel SMITH 8 Feb 1792; Elias SMITH 25 Mar 1796; Jerusha SMITH 2 May 1804; Elisha SMITH 11 May 1806; all born in West Haven with father Joseph and no mother named.

A user-submitted family tree on Familysearch.org ( https://familysearch.org/pal:/MM9.2.1/MWJ4-QM2 ) shows parents Joseph & Olive SMITH. But it states that Oliver’s wife was Adaline DIRED, married 1 May 1830, New Haven, Addison, Vermont. It’s conceivable that he had 2 wives; it wasn’t until 1850 that his wife Deborah was named in the census. Joseph’s father supposedly was Supream SMITH b.1737, son of Stephen SMITH b.1707, son of Nathaniel SMITH b.1675, son of Nathaniel SMITH b.1639, son of James SMITH b.1610. No sources cited for that tree. See page 19 in "John Stoddard of Wethersfield, Conn., and his descendants, 1642-1872 : a genealogy" Newark Valley? N.Y.: unknown, 1873, 90 pgs. Book available at HeritageQuest Online. Page 19 links Joseph SMITH to Stephen SMITH & Mary STODDARD.

Some researchers point to the marriage of Olive Moore and Joseph SMITH, 29 Mar 1827, in Sudbury, Massachusettes, as the parents of Oliver, but this was 2 years after Ephraim T. SMITH was born.

Ancestry.com: "Connecticut Town Birth Records, pre-1870 (Barbour Collection)" has a birth record for Joseph SMITH, b. 30 Jan 1768, Litchfield, CT, son of Supream SMITH, with a reference to Vol.1, p.163, Litchfield Vital Records.

1800 census, West Haven, Rutland, Vermont, has a Joseph SMITH, age 26-44 (the above Joseph would have been 32).

The "Lique Mock Family Tree" by member "wmock154" on Ancestry.com has Oliver SMITH b. 1800, dying at age 1, so a dead end based on that tree.
Some online trees have Supream SMITH also dying at age 1.

Find A Grave Memorial# 70187503 claims that Joseph's wife was Olive MOORE (1772-1811). Subject of this memorial was brother of Oliver (1800-1830).