You can't get a co.jp name unless you have a company in Japan. The cheapest way around this is to have a company in the US and do a branch office in Japan. You're also only allowed 1 per company.
These restrictions do not apply to "jp" addresses.
For .jp addresses, the cheapest I've seen in English is about $125 (US Dollars). The cheapest I've seen in Japanese is 4500 yen (about $40) but that was part of a hosting contract, and there's nothing cheap about hosting in Japan.
On this note, though, I noticed today that every search I could think of on www.msn.co.jp would give me ONLY results that ended in .jp ... which is disconcerting, seeing as a ton of Japanese use that as their first search option.
I haven't found the 4,500 .jp registration yet, so I can't verify that it's real.
The cheapest I've found so far is this:
. jp registration, one year: 7,950 yen, two years: 13,980 yen.
Updating for 1 year: 6,880 yen; updating for 2 years: 12,880 yen. (This doesn't include tax, which is about 5% I think.)
"Updating" means extending or renewing it. 7,950 yen is $66.38 in US dollars at today's exchange rate (see www.xe.com for exchange rates). This is cheaper than the $100 per year I saw at register.com and the $140 per year at another registry.
.co.jp registration is more expensive: 19,048 yen for 1 year. The renewal though is just 6,667 yen.