It could be a bad needle and seat, or misadjusted gas-soaked floats. When was the last rebuild on the carb?
Lastly, depending on the year of the engine, and what it came out of (a 360 wasn't a factory option for a CJ), the carb may be set up to have "controlled vacuum leaks". For example, a charcoal canister is a controlled leak because it doesn't hold vacuum. Therefore, the leak adds air to the A/F mixture, by design. If you, or a PO, disconnected and plugged this "controlled leak", the carb would run rich.