I think this will be very tough to find in an online vendor, if not impossible, since 3x5 and 4x6 are the common sizes you see.

If it's a rug with an all over pattern, and not with a border that would be affected by cutting down, I'd probably buy the 4 x 6 and have it cut and bound locally, after sending a link to it to a local rug cleaner who does that service. Rug cleaners in my area do repairs, sizing and adding fringe, as well as binding.

No border and all over pattern.

I was hoping to find an online seller who also does what the local guys do? Or maybe a vendor who buys a big roll of the stuff before it is broken into standard size rugs and bound?

I don't live in an area with lots of services.

Here is a site with a selection of 4x4 rugs. Where you select size, you have to scroll down below the larger sizes and there is a 4' square option. Good luck!

Here is a link that might be useful: Modern rugs

I just ordered a rug from Naturalarearugs.com ---
custom size seagrass. I don't know what else is available through them - I have not yet received it - but it was great - because I ordered some samples (really cheap) - then ordered the size I needed ---
I am not affiliated with this company ---- just placed an order and looking forward to receiving it - and you can get $25 off your first order if over $100 and free shipping.