Original spelling would be POSAVEC, in this case the C has no diacritical mark over it giving it the sound of TZ or TS as in the word cats.
Correct spelling is Anton, not Antone. This is borne out in the 1930 US census
Anton Posavetz 43 arr. US 1910 Serbian
Josephine Posavetz 42 arr US 1906 Serbian
Anthony Posavetz 15
Josephine Posavetz 10
Loreda Posavetz 4
I would doubt they were Serbian. PIRC is a typical Slovenian name and POSAVEC can be Slovenian or Croatian
Anton was from Trgovišče, Slovenia located 79.6 miles ENE of Ljubljana http://www.mapquest.com/?le=t&q=46.4161%2C16.0961&zo...
This area was NOT Kustenland, it was part of Krain, but is NOW Slovenia, which is where you will want to post your messages and where you will find records, not Austria.
Josepine may be Josefa or Josefina in Slovenian
I find no record for her arrival in 1909, however the closest match is
First Name: Josefa
Last Name: Pirc
Last Place of Residence: Austria
Date of Arrival: Nov 13, 1906
Age at Arrival: 18y Gender: F Marital Status: S
Ship of Travel: Kroonland
Port of Departure: Antwerp
Manifest Line Number: 0017
Destination to her sister Marija HRIBAR
Anton filed Naturalization papers in 1926