What happens when there's no specific input variable on a logic diagram using a JK flip flop?
Your instinct is correct - assign labels to the FF outputs, e.g., Q1 and Q2. To form a state table, on the left side, list the the four possible states of Q1, Q2; on the right side, write the values that Q1 and Q2 will assume after the next clock pulse. The table will then contain a complete description of the state machine.