there are different sizes. best way to measure. would be to use a digital caliper. if you have a local machine shop or a napa or somethin. im sure they would be glad to measure it for you. then when you order your adapter, tell them the measurements.
what kind is it? bendix? call piston bikes, pirate or sportsman flyer and tell them what kind you have.
most of the manufacturers and suppliers will be able to tell you if they have one that fits if it's a common hub.
that wheel will work. you should find out what kind of hub it has, you didn't say.
the shimano CBE-110 is miles ahead of any other coaster brake currently available. the cheaper brands (histop, falcon, KT, etc) all have been known to self destruct.
you can use the kit sprocket with the adapter, but you have to very carefully drill new holes. gotta make sure they're perfect or your sprocket will be out of round, and the chain won't stay on.
Another coaster hub they don't make sprocket adapters for is the 3 speed Nexus SG-3C41.
It measures 1.86" and like the OP said, all of them only go up to about 1.5". Too bad, but, I've never had one problem with my trusty old rag joints. I just wanted the aluminum adapter for the looks on my Nirve chopper.
Tom
I've used the cbiio hub adapter on two Bendix hubs. Both hubs were salvaged from middleweights and neither one had the band (red, yellow, whatever) that some of the later ones had. So this model is smooth with no band and is a smaller diameter than the later Bendix hubs. These are well made hubs which I laced iinto rims replacing the Histop hubs (same diameter). I had one Histop self destruct on a wheelmaster wheel. Open up the Bendix and the Histop hubs and compare the quality of metal and bearings... what a difference!
The Bendix hub I'm referring to in this post would have been the first ones they made with the modern tooth pattern... not a skip tooth, and both of mine were from middleweights. Worth salvaging for sure. I know I tossed several of them before realizing I could lace them into balloon tire rims and use the CB110 adapter. Wish I hadn't thrown those away. There are PDF files on the internet showing the parts inside, so cleaning them up and repacking the bearings is a breeze. Neither of the ones I did showed any signs of wear in spite of being forty some years old.
SB
This is probably the best thing to do. Since you want to buy a sprocket adapter anyway, just buy this one and you get a better wheel at the same time for not much more frog skins.
http://www.piratecycles1.com/cbwhw12gasps.html