Ellis Island did not open until 1892, so you will not find them in that database.
If they were Slovenian the name was more likely originally spelled KOCEVAR, which sounds like kohchevar.
Is this your GGgrandfather as found on a Kane Co IL Naturalization Index Card?
Name: John Kocevar
Birth Date: 31 Oct 1867
Birth Place: Austria
Age at event: 49
Court District: Illinois, Indiana, Wisconsin, Iowa
Date of Action: 19 Sep 1917
Residence 408 S. Lake St, Aurora, Kane Co. IL
If this is him then you need to locate his Naturalization Paperwork which ought to give his birthplace and the date and ship of arrival in the US
According to the Rev. Trunk (a turn of the century Slovenian priest in America) KOCEVAR in Pueblo CO, may have come from Bela Krajna region of south Slovenia, next to the Croatian border
I find no such family in the 1870 IL census. What was the spelling of their name in the census? In which county did the live?