Clicking sound

-edited to correct description

I have a 1999 Cavalier with a 5-speed manual and about 240,000 miles. It makes what I’d call a dull clicking or popping sound, mostly when I accelerate after upshifting or starting from a stop. It also does it sometimes when I let off the accelerator, and then clicks again when I accelerate again. It happens more when it’s cold and just about goes away on a longer drive. The sound occurs once and is not repetitive.

I put the car up on ramps and inspected the underside. Between the inner CV joint on the passenger side drive axle and the differential there’s some play. It can wiggle up and down a bit. On the other axle, there’s no play at all. I replaced the passenger side wheel bearing a year or two ago, everything else from the wheels to the engine is original. All CV joint boots are in good condition. I found no other evident problems.

Do you think the play between the drive axle and differential could be causing this sound? Any other ideas, or possible corrective actions? Thanks in advance.