Below is a piece about the unit from Dyer's and then some info on Frank Revoire of the 4th USRC.
4th REGIMENT MO UNITED STATES RESERVE CORPS INFANTRY.--(3 MONTHS.)
Organized at St. Louis, Mo., May 8, 1861. Attached to Lyons' Command, Army of the West. Capture of Camp Jackson, St. Louis, May 10. Ordered to Rolla, Mo., May 16, and duty there till June 30. (Cos. "A" and "B" at garrison, Waynesville, till June 30.) March to Springfield, Mo., July 1-5 (except Co. "C" at Waynesville and Co. "L" at Lebanon). March to Mt. Vernon to reinforce General Sigel July 7. Return to Springfield July 9. Moved to St. Louis July 17. To Bird's Point, Mo., July 18, and duty there till August. Mustered out August 18, 1861.
Regiment lost during service 4 Enlisted men killed and 6 Enlisted men by disease.
Source of Data: "A Compendium of the War of the Rebellion, V.III" by Frederick H. Dyer, c1908, p.1324
National Park Service Soldiers and Sailors system also lists a Francis Rivoire with the 17th Mass Inf. I suspect that this is a different man than the Frank Rivoire of the 4th MO USRC, mostly because the service interval overlaps.
From "The German Cause in St. Louis" http://www.missouricivilwarmuseum.org/germancause.htm
"FOURTH REGIMENT, UNITED STATES RESERVE CORPS, MISSOURI VOLUNTEERS,
mustered May 8, under President Lincoln's Order of April 30, with eleven Companies, chiefly from the neighborhood of Franklin avenue, by electing B. Gratz BROWN Colonel and establishing an Amory and Headquarters at Uhrig's Cave, southwest corner of Washington and Jefferson avenues. On May 10 it held the northeastern approaches of town to Camp Jackson. In June and July it secured the route, via Rolla, to the Southwest, where transports had to provision the Army over 120 miles of wagon road. The Regiment met Sigel on his retreat from Carthage to Springfield at Mount Vernon. Of the 11 Companies of the Regiment, one was comprised almost entirely of Americans, and one of Frenchmen; of the entire body 75 per cent were Germans.
Mustered out at the expiration of service in August, six Companies reorganized for the Reserve Service in September, under Lieutenant-Colonel John H. HERDER, but were already, in January, 1862, consolidated with the Eighteenth Missouri Volunteers. The Regiment mustered for the Three Months' Service 1014 men."
Rivoire is a french name and I suspect Frank Rivoire was a part of the french company listed above.
The Frank Rivoire of Missouri USRC service is listed on the 1890 Vets Schedule as being alive and well in 1890 living in dwelling 271 at 2017 S. Jefferson Ave. St. Louis Missouri. In the 1890 city directory he is running a wine business at 612 Spruce St. He is found with wife Clotilda in the 1870 Census Stlouis Ward 5, born about 1835, working as a carpenter with his wife and 3 y/o son Lucia. He and his wife are listed as 1860 immigrants from France both being born in France. He is again found in the 1900 St. Louis census with wife and 17 y/o son Aristides again reporting immigration in 1860 from France. He and Clotilda are again listed in the 1910 St. Louis Census.
Lucia F Rivoire has a WWI draft card showing him married to Mary Rivoire and living in Philadelphia PA in 1918. This is confirmed with the 1920 Philadelphia Census. Interestingly he is also listed as working as a bartender at the Martin Hotel in Sioux City Iowa in 1915 as a vetern of the Spanish American War "Co. D, 3rd Mis Regiment" (presumablly Missouri). He is listed with wife Mary A (Mamie) in the 1910 St. Louis Census as a bartender.
Aristides Charles Rivoire is listed in the 1910 St. Louis Census as married to a Emelie F. Rivoire with 2 y/o son Raymond L. He has a WWI service card on file showing Navy service in Philadelphia as a seaman, enlisting in St.Louis 8-26-1918. Residence is listed as 4045 A Shennandoah Ave.
Clotilda Rivoire death certificate indicates she died of Pancreatic cancer on Sept 18, 1914 age 72 being born on April 28, 1842 in France to N. Lecoutour and M. Gain. The certificate lists husband Francois Rivoire as the informant.
As I could not find a 1920 census listing, nor a death certificate listing, and he would have been nearly 86 by then, I suspect Frank died between late 1914 and the mid 1920 census period.
Given the above personal history of Frank Rivoire, from primary sources, I suspect that the individual you have listed as being buried in the Portage Des Sioux Mo cemetery in 1889 is NOT the same Frank/Francois Rivoire vet of the 4th USRC Missouri. If you have further information or other indicators of Civil war service for your Frank/Francis/Francois Rivoire please let me know. For all I know he may be the Massachusetts vet!