Tony:
Princess

Steve:
Mini Rogers

Natasha:
Angel

Bruce:
GreenBeans

Clint:
He has multiple names; BirdBrain, Merida, but mainly Scops (type of Owl)

Pietro:
Roadrunner

Wanda:
Sweetie

Loki:
Wicca or Sass-Queen

Thor:
Little Queen

Bucky:
Monster