Avianca is having another sale from New York to Paraguay with fares starting at USD 956.
These fares book into A class which earns 100% in most Star Alliance programs and gives you 1/5 of distance as PQPs for United. In the case of the sample below JFK-BOG-ASU you would earn 9632 miles and 1926 PQPs.
Here are some links to Trip Reports on Avianca on their Boeing 787 from GRU-BOG and Avianca 330 from BOG-JFK
Avianca Airbus 330 Business Class
Avianca Airbus 320 Business Class
Avianca Boeing 787 Business Class