For PlayStation 2, the only officially licensed Guitar Hero controller is the wired SGX-50 (Gibson SG) model bundled with the original Guitar Hero (2005), Guitar Hero II (2006), and Guitar Hero III: Legends of Rock (2007).
PS3 Guitar Hero controllers (USB) do not work natively on PS2. Adapters exist (e.g., PS2-to-USB converters) but introduce latency and button-mapping issues. Not viable for serious play.
Source an original RedOctane SGX-50 (check eBay, local classifieds, retro game stores). Verify the PS2 connector is intact. For better durability, consider Guitar Hero III Les Paul (PS2) — same connector, improved strum bar.
If you want modern reliability, play Clone Hero on PC with a current-gen controller (Xbox 360/One, PS4/5, or dedicated controllers like the TiltFive).