How to cover dishwasher opening?

How about a rolling cart island that you can store there and take out when needed? Below are some other ideas I came across. Also building a platform and shelves with pretty baskets that you can pull out would give you additional storage.

https://homeguides.sfgate.com/remodel-space-removed-dishwasher-66036.html

If you want to use it for the trash can, there are some tutorials here on Hometalk that show you how to build a trash can cabinet. https://www.hometalk.com/diy/organize/kitchen/hide-your-ugly-trash-can-with-this-brilliant-fix-6018435

https://www.hometalk.com/diy/decorate/diy-pull-out-kitchen-cabinet-trash-can-28652553

Really all you'd need is a "door" that either tilts out or that you put on with full extension drawer guides and pulls out. The door wouldn't have to match your cabinets exactly, but be a complementary color or finish. I think using a curtain might be clumsy and it might get messed up easily.

How about a rolling cart for extra storage? You can make a door, use a curtain or if you have enough space, a barn door?

A tension rod would be an inexpensive way to do a curtain. A spendier option might be to get a cabinet door that would fit the opening and the hardware to make a pull out trash bin. Just like you would do in a cabinet but without the additional cabinet.

I turned mine into another cabinet buy framing it with 2x2" lumber, then I had a pair of cabinet doors that I had taken off another cabinet over the frig that fit perfectly, but you could also probably find some at Habitat for Humanity Restore that would fit. I added a 10" shelf at the back of the opening to increase storage. I use it to store gallons of stuff, and cleaning supplies.

I had an apartment I did the same thing in but I turned that one into a bookcase for all my 100s of cookbooks.

How about a box on low wheels? The box could have a swinging door (or 2 swinging doors) on it and have a sliding rail holder for a trash can on one side and shelves for pots/pans or whatever on the other side. The doors could be painted/finished to match the existing cabinets and would be easy to use. Then if you sell the home or wanted to later put in a dishwasher you could just roll the 'box' cabinet out of the way.

Your trash can idea is a good one, but I would not put a curtain over it. You could get a pull out shelf to put it on and let it be exposed, but in the space, and with that, you could also have a recycling bin behind it. Here is what they look like: https://www.amazon.com/s/?ie=UTF8&keywords=trash+pullout+for+cabinet&tag=googhydr-20&index=aps&hvadid=229781281374&hvpos=1t2&hvnetw=g&hvrand=6919929278987989981&hvpone=&hvptwo=&hvqmt=b&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9028716&hvtargid=kwd-377834141654&ref=pd_sl_1fnquh1n55_b_p38. You could also make it shallower and put in a bookshelf for your cookbooks.

You could use a tension rod and some fabric that goes with the décor in your kitchen. Have two sides to the curtain so that you have easy access to whatever you decide to put in it. If you want, you could even put up a shelf or two to put in some of the small appliances you have on the counter, or you have to get out of a closet to be able to use it. Easy to get to if you want to use it, but out of the way when you don't use it. The space is pretty big for dishwashers, maybe have some shelving behind the garbage can would work. You should be able to cover the opening easily without putting up doors, LeAnne!