A euphemism for penis or dick. Along with being a slight dig at whoever it's used against thanks to the connotations of baloney (cheap, unwanted, undesirable, etc.).
Saying this will also immediately make you friends with any and all weebs who've watched Neon Genesis Evangelion since that's where this phrase originates from (the ADV Dub of the series from 1997 to be exact) to the best of my knowledge. Thank you, Amanda Winn Lee (ADR Script Writer and Voice Actress for Rei Ayanami) for writing and saying this!
Rei: Woaagh! You're the jerk who was staring at my panties!
Asuka: Hey, what do you mean by that?! You're the one who was flashin' them y'know!
Rei: Oh and who are you and why are you defending him? Are you riding his Baloney Pony?
*shock envelopes the classroom*
Asuka: We're just really good childhood friends! You shut up!
Hikari: Be quiet you two! We're in a class, not a bar!
Misato: Hey, this is more entertaining than class! Go on, I want to see how this turns out.
Fogey/fogy /fougi/ sl. (early 18C+, orig. Scot) old-fashioned, stuck-in-the mud.
Person with old fashioned ideas which he is unwilling to change: Come to the disco and stop being such an old fogey!
You think me an old fogeyand an old tory, his thoughtful voice said. I saw three generations since O’Connel’s time. I remember the famine. Do you know that the orange lodges agitated for repeal of the union twenty years before O’Connel did or before the prelates of your communion denounced him as a demagogue? You fenians forget some things. (James Joyce, Ulysses. PenguinBooks,1992. p. 38)