Nine times out of ten it is the belt. Here is the order we work it in on the bench, cheapest and most likely first.
1. The belt itself. Rubber belts stretch and glaze with age, and a glazed or stretched belt is the number one cause of pitch wobble on a belt-drive deck. Measure first: belt sizes for the same deck disagree between sources often enough that the reliable method is measuring your old belt and going slightly smaller, not trusting a forum number for your model.
2. Where the belt sits. A belt riding up on one edge of the motor pulley throws the speed badly; one documented case ran thirty percent fast until the belt was re-seated flat in the pulley groove. Free to check, so check it before buying anything.
3. The motor's run capacitor. On older decks (especially pre-1974 units), a tired motor run capacitor makes the motor stall and overheat, and speed instability is one way that shows up. Small, cheap part; just match it to the motor.
4. Old grease. On idler-drive and some direct-drive designs, hardened lubricant is the hidden villain. Dual idler decks are documented seizing at the speed selector and idler pivots from grease that turned to glue. Degrease before forcing anything, and lubricate properly (never WD40, which is not a lubricant).
One honest caveat: not every wobble is mechanical. Worn stylus and rumble get discussed in the same breath on the turntable boards for a reason. If the wobble changes with a fresh stylus, you have your answer.
Post the model and one detail that helps a lot: does it wobble from the first second, or only after it has been running a while? Cold-versus-warm narrows this fast.