As Bob Jewett said, an easy option is just a rolling duffle bag, and obviously measure your cue case and make sure you get a duffle bag that is long enough for your case. Probably want to even get a duffle bag that is a couple of inches or more longer than your case in case the manufacturer's measurements or manufacturing tolerances aren't precise, and/or so the bag doesn't end up compressing too hard on the ends of your case after you pack it full of clothes and whatever. If your cues are in a hard sided cue case, or one with pvc tubes for the cues, it may not matter as much whether the duffle has a frame structure to it, but I would personally highly prefer it have some kind of a stiff frame structure to it on the bottom (and Bob's warranty suggestion would always be good in case the frame ever breaks). The link below is what they sort of look like (no idea if this one has a frame, is decent quality, or anything else, just linked to it for the picture).
Read reviews and buy Rockland 40" Rolling Duffel Bag at Target. Choose from contactless Same Day Delivery, Drive Up and more.
www.target.com
As t.wallace said, some regular suitcases will fit the case diagonally which is also what I use to travel with my. As Bob already noted, most airlines have a limit of 62" for size of your suitcase when the length, width, and height are added together. But the suitcase models out there, even the ones that all add up to 62", vary in their exact dimensions. One might be 28x20x14 (adds up to 62), and another might be 32x20x10 (also 62). You want to look for the longest ones, because the longer it is, the more room there will end up being for your case to fit in there diagonally.
Also, once you find one that looks like it might work, do the math to calculate what the diagonal measurement would be preferably by using the internal measurements instead of external when you have them (this will do the math for you if needed
https://www.calculatorsoup.com/calculators/geometry-plane/rectangle.php) to verify that your cue case will indeed fit, and allow for needing at least an additional inch or two on the needed diagonal measurement if possible in case your cue case can't get all the way into the very tip corners of the suitcase due to the width of your cue case (especially with hard sided suitcases). Getting a couple of extra inches of diagonal room on top of that it is even better (to avoid possible compression on the ends of your cue case) but depending on the size of your cue case that might not happen in this style from my experience of looking around at their dimensions in the past (there aren't a ton of them out there that are going to fit your cue case diagonally at all, and fewer yet that would give you very much extra diagonal room).
Also, if you stay with the soft sided suitcase style rather than hard sided (but a good frame on the bottom is still desired) your cue case will likely fit even if the diagonal measurement is exactly the same as your cue case (or perhaps even a touch shorter than your case length but you are starting to really gamble) because your cue case will just push those corners out enough to still be able to get it jammed in there but this certainly wouldn't be preferred if you can just find one big enough without having to do that (and this may not even be a worthy last resort option depending on what kind of cue case you have and how much you care about the longevity of your suitcase or cue case). Below is a link to the soft sided style I am referring to, but again this is for picture reference only and I don't know that this particular one would fit your case.
Read reviews and buy Skyline Softside Large Checked Spinner Suitcase - Gray at Target. Choose from contactless Same Day Delivery, Drive Up and more.
www.target.com