Your family is Lutheran and I found Carl's burial at Concordia Cemetery through the Trinity Lutheran Church website which has records available on-line. http://www.trinitystlouis.com/genealogy
Under Niemeyer Carl who was buried Oct 19, 1879 and died at the age of 52 yrs, 9 months and 14 days. Most importantly, he was buried in Sect 2A Lot 154 and several others are buried there too: primarily children who died in 1863, 1864, 1866, 1868 and a Gertrude F. Niemeyer buried Apr 12, 1909 at the age of 39 years and 10 months, as well as his son, Henry L. Niemeyer on Nov 11, 1942 at the age of 90.
The St. Louis County Library Hqs Genealogy Dept has on-line indexes including one for the Immanuel Lutheran church baptisms:http://www.slcl.org/content/baptisms-n-immanuel-lutheran-chu...
There is a Carl Friedrich Wilhelm Niemeier who was buried in Concordia cemetery in the same plot above and who was baptized at Immanuel Lutheran. If you have not ordered the church records for Immanuel Lutheran, I suggest you do so in order to identify what additional info can be gleaned from their children's baptismal records as well as if any of them appear in the burial or marriage records too and who served as witnesses, etc. The Family History film numbers are listed on the index noted above.
Have you checked the church burial records for Sophia in Arkansas? German obits in local German newspapers? Have
you been able to find their passenger list record?
Apparently, their son, Henry was married several times - it is possible that his marriage records might indicate where he was born in Germany - I would also pursue that research.
Hope this helps,