MC1496 can be used as a DSB SC and AM IC, but their circuits on the datasheet are the exact same. What is the difference between the two?
To check:

be sure you DC_block the modulating input

alter the gain, by using 100 ohms between pins 2 and pin 3

if not over a Ground plane with good VDD bypassing, then phase_shifts vi the power rail might upset the internal charge cancellations that produce the carrier suppression