They’re the Stone Ponies, as in rocks. Not Stoned Ponies, as in altered states of consciousness.
I believe the name originated with Hugh Browne, who contributed to several earlier BattleTech products. I gamed with him in Boston. He was a Linda Ronstadt fan, and her first band was a trio called the Stone Poneys. (Spelled differently.) Hugh thought it was a good name for a merc unit, and IIRC, submitted a write-up for Field Manual: Mercenaries or some earlier mercenary sourcebook. Although that write-up did not make the cut, the name was picked up later for Merc Supp II and someone else did that write-up. (Same thing happened to me with Gray’s Ghosts and some other merc units.) Apparently they figured out the connection, and named the Stone Ponies CO Lyndsey Reinstadt, an obvious allusion to Linda Ronstadt.
AFAIK, the Stone Ponies have not appeared anywhere else. They and other Merc Supp II units (like Gray’s Ghosts) were written up as Jihad canon fodder/Blakist contractors and so did not have long lives.
Hope this helps.
As far as I can tell, the Stone Ponies only show up in Mercenaries Supplemental II and Mercenaries Supplemental Update (I have neither, I looked them up on Sarna)
Unless I missed something, Sarna is in error regrading Mercs Supp Update. The Stone Ponies do not appear in the ToC, write-ups, roster, or special unit rules for that product.