From Michigan Place Names
Clinton County: first settled by John Ferdon in 1836; he was a member of the Rochester Colony which founded Duplain, his land lying in both Duplain and Greenbush Townships; before platting, the place was known as Williamsport (for pioneer settler Clark Williams), Barrington (for another pioneer settler, J. A. Barrington), and Swizzletown (which suggests the inhabitants were bibulous). Platted in 1857 by Isaac Eagles and Mr. Barrington who named it Greenbush after the township which had been given a post office of that name on Jan. 29, 1844, with Lyman M. Richmond as its first postmaster; on May 9, 1867, both post office and village were renamed Eureka, Greek for I have found it; Edward Stark gave it the new name as a place where he had found and others would find a fine place for doing business [Ellis; Daboll; PO Archives)
From Wikipedia
Eureka (/jɜːriːkʌ/ yer-REE-kuh) is an unincorporated community and census-designated place (CDP) in Clinton County in the U.S. state of Michigan. The community is located within Greenbush Township. As an unincorporated community, Eureka has no legal autonomy of its own but does have its own post office with the 48833 ZIP Code.
Eureka is located in northeastern Greenbush Township in Clinton County. It is centrally located in the state's Lower Peninsula about 30 miles (48 km) north of Lansing and 40 miles (64 km) south of Mount Pleasant.
U.S. Route 127 runs south–north about 3.0 miles (4.8 km) west of the community and is accessible via Maple Rapids Road. Other nearby communities include the village of Maple Rapids to the west, the village of Elsie to the east, the village of Ashley to the north, and the cities of Ovid and St. Johns to the south. Halterman Creek flows through the community.
Eureka is served by St. Johns Public Schools. Eureka Elementary School is located within the community. The community has its own post office using the 48833 ZIP Code, although this post office is primarily used for post office box services. The St. Johns 48879 ZIP Code also serves the community. Areas to the east of Welling Road may use the Elsie 48831 ZIP Code.
The area was first settled in 1836 by John Ferdon. The new settlement was first known as Williamsport after early settler Clark Williams. The community was soon known as Barrington for another settler J. A. Barrington. Again, the community's name was known as Swizzletown. The community received its first post office under the name Greenbush on January 29, 1844, which was named after the township. On May 9, 1867, the post office and community were renamed Eureka, which was the name given by Edward Stark using the word eureka "as a place where he had found and others would find a fine place for doing business."
The post office was discontinued on June 29, 1935. It was ultimately reestablished on September 6, 1949. The post office remains in operation and is located at 7907 North Welling Road in the center of the community.
The Eureka Cemetery is located on Hyde Road just south of the center of the community. The cemetery remains active, and its oldest gravesite dates back to 1839.
For the 2020 census, Eureka was included as a newly-listed census-designated place, which is included for statistical purposes only. Eureka continues to remain an unincorporated community with no legal autonomy of its own.