Green’s Dictionary of Slang

a grudge; esp. in phr. have a downer on.

1906		Marvel 13 Oct. 334: He’s got a downer on us.
1999		Indep. 3 Nov. 22: I’ve probably got a downer on him because people were comparing him to Ian Callaghan.
2001		K. Sampson Outlaws (ms.) 127: I try to busk it with him, try to sound like I’ve got half a downer on him for even thinking badly about myself.