"Singative" is like "talkative" or the newly founded "textative."
"Singative" refers to the feeling when someone wants to (or actually does) start singing (either randomly or because they have a reason for doing so).
Jake: Hey dude, why is Melody singing in the middle of the living room? I mean, she's just terrible!
Ryan: Yeah, she does suck at singing, but I can't stop her. She said she's in a singative mood.
Jake: Oh brother!
Ryan: Tell me about it! **Rolls eyes**