Passenger window will go down ok but when going up it may stop half way. At that point it won’t go down either. After a few minutes I can try again and it will go a little higher but may have to do it a few times. Assuming there is a circuit breaker in the motor that is cutting power but don't see any binding or sticking in the window itself. Is the motor just worn out? What brand replacement on Rock Auto is a good choice?
Your power window motor is failing and it is exhibiting the classic symptom of failure. I have two 1996 Cavalier convertibles and I have replaced every power window motor on both cars at least once. (I'm shocked that you haven't had to replace them before-- though if you bought it used, perhaps someone else already has and saved you the trouble of drilling out the rivets.) I've replaced them so many times that the last time I bought a new motor, I bought a 2-pack ($31 on Ebay) because it's just a matter of time before another one fails. If you plan to do the work yourself, following is a link to instructions that I wrote-up for my convertible years ago. I suggest that you read through the entire thread (at least my subsequent comments) because:
1) After doing it several more times, I noted some helpful revisions, like gently, clamping the window up (in place) with rubber-padded clamps so that you don't need to go through the hassle of removing the window and don't risk the window breaking from coming crashing down after you remove the rivets from the regulator. Clamping the window in place eliminates the need for steps #9, 11, 12, 13, 14,15, 38, 39, 40, & 41, at least.
2) I re-posted the helpful photos in a link (since the photos in the original post no longer appear).
If the power window motor hasn't completely failed, you should be able to have a helper manually help the window move up or down so that you can close the window until you replace the motor, and so that you can lower the window to the ideal spot (about 3/4 of the way down, IIRC) where you can easily access the nuts that hold the window to the regulator (through the access-holes in the inner-door-panel). The last time that one of my power window motors failed, it failed completely and was stuck in the full-up position- which made it more difficult to remove the nuts that hold the window to the regulator.
Just got it done today. Bought an AC Delco motor on Amazon for $28 shipped. Although it's made in China, I assume it's better quality than the slightly cheaper off brands. Heard that some of the others are loud and sound crude. This one is quiet. Took about 2 hours. Motor didn't include the rivets to mount the regulator to the door but I bought a box of 25 on Ebay the last time I replaced a GM motor so had them on hand. Way better and easier than messing with nuts and bolts. Didn't have to remove the glass, just secured it with a pair of suctions cups so it wouldn't slide down.
It's a little bit easier to rivet in the new motor but it's a lot harder to drill out the rivets if you ever have to do it again. Unfortunately, I've had to replace them several times, but we raise/lower our tops & windows frequently due to the nice weather here in Silicon Valley.
I also read some power-window-motor reviews that complained of noise and slowness, but I've never noticed a difference between brands in performance or longevity.
Smart move on the suction cups.
If your driver side window doesn't seal properly (at the top-rear against the roof) you may want to consider following my guide to fix that problem.
If you'll be keeping the car for a while, you may want to note this guide on how to replace the convertible top motors. (They have failed on both of my Cavalier convertibles.)
I just swapped mine with crank windows when they failed the first time. With only 2 windows it's not much of an inconvenience to roll them down manually.
2000 Cavalier Coupe, 138k miles, 2.2 Auto, Silver (alive)
1999 Cavalier Sedan, 237k miles, 2.2 Auto, White (dead)
Kinda like swapping in a hand crank when the starter motor fails. Guess it's not much of an inconvenience to hand crank your engine? They did it all the time 100 years ago. But really, in the time it took to cut and modify a door panel you could have replaced the window motor and be good for another 10+ years.
Also, I think the regulator on the convertible is slightly different than the hard top so I don't think one could reasonably convert to a manual crank.