do you mean South-Styria of present Austria or Lower-Styria/Untersteiermark of Austria-Hungary, which is now slovenian?
http://www.winereviewonline.com/south_styria.cfm
http://en.wikipedia.org/wiki/Styria_%28Slovenia%29

you need a placename to ask at roman.cath. diocesan-archive.
and was the slovenian lastname possible Pevec not Pivec?
Pevec means in slovenian singer.

Ellisisland
Pevec: http://www.ellisisland.org/search/matchMore.asp?MID=16900218...
Pivec: http://www.ellisisland.org/search/matchMore.asp?MID=16900218...