Here's the signal you describe, with a perfectly stable trigger on my 3054A.
The trick is to set the holdoff correctly. You want the scope to trigger when the waveform first crosses the trigger threshold, but then to not re-arm the trigger circuit again until after that particular AM cycle has decayed away. In this example, the amplitude of the AM signal exceeds the trigger level for a period of about 4ms per cycle, so by setting the holdoff to 5ms I ensure that when the scope has triggered once, it won't trigger again until the next cycle reaches the necessary amplitude.