Heres a information site www.efloras.org I cant find a site that sells them. If you happen to come acrost a site that sells them tell me.
From what I have been able to find there are only a couple of places that have it in their collections in the US. One being the Quarry Hill Botanical Garden. It seems more widely available in the UK. I was surprised that Piroche did not carry it though. I am guessing that the best possibility will be a seed source with the USDA import restrictions.
Heritage Seedlings, a wholesale grower in Oregon, has tried propagating it from seed (which is also pretty rare) with little success. They hope to eventually get a stock plant so they can graft it onto another carpinus. This is the company that introduced Carpinus japonica and other interesting Asian hornbeams to US growers.
I wonder if Heritage really was the first to wholesale C. japonica here, it's been on the continent since before 1890.
Maybe not the first wholesaler, but very influential in making it common (at least in the Northwest). In the early nineties, they were actively promoting it to growers; at the time, it was very rare in the trade, now, it is very common.