Tony- Tiger
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Steve- Sweetheart
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Natasha- Butterfly

((She typically says your nickname in Russian though.))
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Bruce- Sunshine
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Clint- Nathaniel's nickname is trouble while yours is Angel
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Wanda- Cutie

((She typically says your nickname in Russian though and Vision doesn't call you a nickname.))
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Pietro- Roadrunner
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Thor- My daughter

((He doesn't really understand the concept of nicknames))
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Loki- Snowflake
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Bucky- Bear Cub
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Falcon- Birdie
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Rhodey- Kiddo
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Spider Man- Bug
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Wolverine- Lil' bit
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Coulson- Smiles
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Deadpool- let's be honest here. We're talking about Deadpool... he keeps changing your nickname so you don't exactly have one.
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Dr. Strange- Silly girl
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Guardians of the Galaxy- Spaz
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Nebula- Nebula mainly just calls you by your name.
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Black Panther- Princess
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Nick Fury- Baby girl
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Agent May- (Nickname)
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Skye- Sweetie
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Fitzsimmons- Monkey (Fitz) Love (Simmons)