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.
A substitute to the word "lie/s" and to a extent "bullshit". When presented with false-hood information and wanting to declare that all that was said is classified as a lie.
Whats with all the "phoney baloney" that your providing me with, I trusted you with my posessions and i blatantly see a dent on my car.
Thats "phoney baloney" to your claim of being hurt from my mini jab to your shoulder