If you wife has a permanent residency card (green card) and is out of the country for already APPROVED extended period, it can extended via. the local consulate or embassy. I am assuming you do not have a permit. (re-entry permits do not exist with green card holders.) Given it has been two years already, you may have difficulty in Paraguay justifying it without documentation. The best option usually to return to the United States.
I would call or e-mail the Embassy and ask for Citizen Services. They can tell you the best route.
1776 Mariscal Lopez Avenue
Asunción, Paraguay
Tel: 595 21 213-715, 595 21 248-3000
Questions about Visas - For inquiries related to visas, please send an email to paraguayvisas@state.gov.
Consular Affairs For inquiries about passports and any other consular issue, send an email to paraguayacs@state.gov.

Matt V. - Manaus, Amazonas, Brasil
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