The first thing I'd do is look for further records to their place of origin - records created at different times, as well as records created for different people who may have come from the same area. For example, if when they arrived in the US they mention a friend or relative as contact, that person likely came from the same area of Poland and their records may give you a hint as to the area you need to be looking at.
So, presumably you're after these Bilans, Jan and Josefa, who arrived in 1913 on the Lapland. Jan or John Bilan naturalised in the 1930s, and his declaration of intention can be found here. It can be confirmed to be the same person as the arrival as he gives the exact date and ship name. This document is typewritten and gives several locations:
- Bankowszczyzna, Poland, the location of his birth in 1891, as well as the place he claims to be last resident before emigration. This place is in Lublin Voivodeship. Examining it on Google maps shows there is a small settlement called Czarnoziem just to the south-west.
- Krasnystaw, Poland, the location of his marriage in 1913 just before emigration. This appears to be a slightly larger town, further south-west still from Czarnoziem.
- Hendryszyn, Poland, the location of Josefa/Josephine's birth. This I'm struggling to find but presumably was in the same area.
Based off this, I would say that Czarnoziem is very likely your Czaruazien, in the area where Jan Bilan's family originated from. You can probably locate Hendryszyn if you can get a historical gazetteer or map for this region and look at settlements in the Krasnystaw area.