I'm not sure what you mean by a cover, but there is the '58 pattern water bottle pouch which can only be fitted to a '58 belt, unless you modify it, or there is a similar version with high and low belt loops, known as SAS pouches, but I haven't seen these for ages. Then there is the PLCE water bottle pouch which is far better than the '58, because the bottle actually fits in it!
Maybe a '58 bottle will fit in an American pouch. It's worth a try if you can find one in a surplus store. If you want to use the mug that goes with it, I think the only way to do it is to use a PLCE pouch. Arktis should do an aftermarket version which is probably better.
Julian.