Charmed

While Prue helps Piper select an outfit for the reunion party, Piper suggests that they go back to the Betsey Johnson dress.
Betsey Johnson is a fashion designer best known for her feminine and whimsical designs. She also is known for doing a cartwheel at the end of her fashion shows.

When Prue and Phoebe take a possessed Piper from the club, Phoebe says to the party guests "talk amongst yourself".
This is a reference to the Mike Myers' character Linda Richman on Saturday Night Live. Whenever Linda would get upset, she would put her hand on her chest and say "I'm all verklempt" or "I'm a little verklempt". Then she would say, "Talk amongst yourselves," sometimes waving her hand in a dismissive gesture toward the audience. She would often follow this with an example, by saying, "I'll give you a topic."

Prue refers to Piper being "like Jan Brady".
Jan Brady was the middle sister in the TV series The Brady Bunch, that ran from 1969-1974.

Title: Coyote Piper
This is a reference to the 2000 movie Coyote Ugly, which is emulated in the bar dance that is performed by Piper while possessed. It could also refer to the trickster spirit of the Western United States Coyote who often delighted in taking on the forms of different people and animals. It seems rather fitting as Terra does the same in this episode.