You could put a rug on the grass, but I can't image how it would not get moldy - plus, I don't think the furniture would be all that level. How much do you have to spend? Maybe pull out the grass and add pea gravel - that would be an inexpensive solution ...

I saw this once before and the rug was bunch as the ground was not level. Once they put the furniture on it, the rug would fold up in some areas. Plus, I would consider how you cut the grass around it. The rug would instantly get ripped by a lawnmower the first time around.

Carpet straight on the ground gets lumpy. Also can get heavy from soaking up dirt and rain. Sure does kill the crap out of what's under it, I use it to an extent in one of my garden areas for walkways and kill areas.

If you mean to do this as a temporary measure for this summer only, you might be able to get away with laying down a couple sheets of good plywood and then the rug on that. Depending on how level the area is to begin with that is- if the area isn't already fairly level, the plywood trick won't work.

We have pea gravel in another area so I think it would look silly. Just trying to think creatively....

Do you have any pictures?

Sofa area - there’s pea gravel on other side of yard you can’t see

I agree with the first suggestion of pea gravel and think it can look nice.

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You'd need to do quite a bit of pea gravel to make it look nice in that area.

In the meantime, this won't level it but:

https://www.rugstreet.com/PROD/blue-breathable-mat.html

That’s pool equipment not storage bins. It’s permanent equipment ... sorry!

I agree with the pea gravel idea. Since you are not quite keen on that idea do an internet search for Patio Deck out of wooden pallets.

One thing that will make your whole area really pop is to pressure wash your concrete, and look into ”Wet and Forget” to keep the area looking fresh.

Because you could put a "rug" on the grass doesn't mean you should. An actual rug will get really icky fairly quickly. A better "rug" purchase idea might be artificial grass rather than a traditional rug, even an indoor/outdoor one.

If you want the area where you set the sofa and chairs level -- whether grass or artificial turf or gravel, then you m ight want to outline the area you choose for the sofa, etc., with pavers and raise the back of the space to make the area on which the sofa sits more level -- but leave the area behind it and beside it sloped. A short knee wall behind the sofa with just the beginning of a corner/side could help with this: a " [ " shaped knee wall behind the sofa -- and you could still leave the area grassy but more level.

https://www.pinterest.com/pin/336995984586777804/

If you create a planting area below the knee wall to hide the wall, it could visually disappear and keep the green space vibe you seem to seek for your outdoor living room..

You might also consider not leaving the sofa in the exact same place every day. Could you pick three places and move the sofa from one to the other every couple of days? Would what the sofa is made of mean it would be practical to add wheels to make it easier to do that?

You might also consider not keeping the entire set together. For instance, the coffee table would block any sunlight that might otherwise shine on the first several inches in front of and beneath the sofa early/late in the day. Ditto that the chairs from the side.

Another idea might be a raised treated wood deck with pea gravel beneath it; however, low decks can have moisture issues and attract pests that wan to hide beneath them, including snakes. Would not really recommend this.

As a cheap, temporary fix, people have used wall-to-wall carpet, upside down, and it works pretty well for setting lightweight furniture on it. (Better than just dirt or grass.) Then put the outdoor rug, for decorative purposes, on top of the that. A common outdoor rug or mat alone is too thin and flimsy. Talk to a carpet installer as they haul out and throw away used carpeting all the time. Also, I've seen people offering it on craigslist.

I would totally move the sofa and chairs over to the concrete patio area. They don't work at all on grass, and once you start adding pea gravel to a grassy area, you can never keep it contained and it will be difficult to mow the lawn. It's very messy.

Go with patio stones. They are not expensive and are better than pea gravel with the pool near by. You said the ground is too lumpy for patio stones. You have to prepare a good base to lay patio stones, they don’t just get laid on top of grass! Once you dig the base and lay gravel then sand, you can lay the patio stones for a flat surface. Patio stones come in a variety of shapes and sizes these days. One or two weekends of work and you’ll be done and won’t have spent a lot of money.

Can‘t move the pool equipment. Darn. Had another idea, we added flagstone and did it ourselves. An easy job and not expensive when you do it yourself. Just have to cut out grass and level underneath.

You could rent a sod remover and get rid of the turf to start. If you are not in a situation to put in something permanent, you could buy outdoor wooden walkway slats or squares to put over the newly exposed dirt, weeds will eventually start growing underneath but you can pick up the slats from time to time to pull weeds or spray weedkiller if you are OK about using chemicals. It's a short term fix for sure but maybe it could help you get through the season. Cutting the lawn in your yard's current state must be a pain having to move all that stuff you have on the grass.