It is highly probable that the name originally started out as Kohlenbrenner (the 1868 Syracuse city directory almost has Roman's name as that) but got shortened sometime around the middle to latter half of the eighteenth century. Some of the more common spelling derivatives are Kohlburner, Kohlrunner, Kohlbrener, Kolburner, Colburn, Kohlburn and a whole host of others where the non-German ear has tried to translate it into English.

We know that the family hailed from the Grand Duchy of Baden which is now part of Germany[1]. Today it is refered to as Baden-Wurttemburg[2] but when Roman left in 1851 it was a Duchy under the reign of Grand Duke Leopold[3]. Two years prior in 1849 a revolution had broken out in Baden, whether this had something to do with Roman emmigrating to the United States, we do not know.

We also do not know precisely where in Baden they came from. The State was predominently Protestant (the Grand Duke was the leader of the Evangelical Church) though the area around Freilburg at the southern end of the state, is home to the Catholic university and the Archbishop of Freilburg. Assuming the family were Roman Catholic when they were in Baden would suggest they lived in the area around Freilburg and why it is difficult finding information about them as very few Roman Catholic records are available online. The death certificates of either Roman, Caroline or Leopold might give their birth place which would be a major boost in finding more early information about the family.

Footnotes:
[1] 18 Jan 1871 saw the unification of various states which created Germany as a country.
[2] The two distinct areas of Baden and Wurrtemburg were united in 1952 after a referendum.
[3] Leopold reigned from 1830 until his death in 1852