The writers took the name "Sunshine" from the original UK QAF

Hazel (Debbie) called Nathan (Justin) "Sunshine once. BUT it was done sarcastically. He was staying with her and was acting up.

When Debbie first saw Justin, calling him "Sunshine" in a nice way made sense because he was young, blond and innocent looking. Randy's personality and smile may have had something to do with the continued use of the nickname , but I think the writers always planned to usei at least once.