Sorry I promise I used the search bar before posting and didn't find this post already on the topic:

Tonneau cover that fits with soft top on?

Hi all, Not sure if I'm looking for something that doesn't exist, but I'd love to find a tonneau cover that can fit while the soft top (OEM Premium Twill top) is in place. It's hot here (Charleston SC) in the summer and I prefer to leave windows zipped out but top on for shade. We also get...

www.wranglerforum.com

Google found it for me though. Mods please delete if you feel appropriate

 

Not sure exactly what you are looking for.
But there's this

Tuffy Security Products Tailgate Security Enclosure for 07-18 Jeep Wrangler JK

Finding the right space for sensitive items and valuables when you are adventuring in your Jeep can be a great challenge for 2 door Wrangler owners. Maximize your cargo space utilization with Tuffy Products Tailgate Security Enclosure specifically for 07-18 JK 2-Door models.

www.quadratec.com

But a 2 door JK doesn't have much behind the rear seats.

 

To make a tonneau that would work with a folded soft top would take a lot of sewing. A sail shop might be able to sew it up but not only would you have to incorporate the equivalent of a Smittybilt boot cover in it but you would also have to have two long inverted U sections that stood proud of the tub rail by 8" or more to cover the frame arms. When you were done, the center part would never be taut and would probably flap in the wind.

You might want to PM @NoGaBiker. He just installed a Master Top cable bimini that he seems to be in love with. Then you could run their bimini too, if you have room to store the soft top.

 

I got notified when BobChase mentioned me, so here I am. Two things:

1) Yes, as he mentioned, I have just replaced my jury-rigged Bimini top with a new Mastertop Plus Twill with cable. Light years better. I wrote a new thread about it last week, with pics, etc. So check that out if Bimini is a reasonable possibility but you were just worried because of all the bad reviews. I said this in my thread — I suspect many of the bad reviews (of all the Bimini/bikini products) result from improper installation.) My thread is probably on Page 3 or 4 by now, or search for Mastertop Bimini Plus.

2) If you’re really rather go the other route and keep your softtop, I have some info that might help. First of all, I use a Jeep Backbone rear cargo cover for my 2-door. That is a “tonneau” cover made of diamond-plate aluminum; it’s the bomb. But it’s six hundred bucks or something and you may not want to go that route for cost reasons. But my point is, I run that deck with my softtop from November to March, i.e. when I take the Bimini top off. I assume your question concerns being able to put the softtop down, is that correct?

If so, your problem is that the frame has to drop down into the tub in order to let the soft top go down the last foot or so. But any sort of cover prevents those frame arms from dropping down in there. The solution is to replace the factory “knuckles” with Rugged Ridge’s quick release version (or you could keep the appropriate tools handy and just remove the factory bolts from the knuckles, but that’s a pain in the ass.) These knuckles allow you to just squeeze them and pull apart, then the frame will come apart at that joint and the top will lie on top of the cover. I honestly don’t know if any given tonneau will support the weight of the top — obviously the Backbone I have will, but a vinyl one may stretch and sag. If that’s the case and you still want to go this route, I’d keep a 1x4 handy that spans the width of the tub, set it down under the stack with it’s ends supported by the tub side rails.

I don’t see why you couldn’t use any of the tonneau covers of choice with the softtop if you use these RR QR knuckles.
Rugged Ridge QR Bow Knuckles