Some have recommended ICDSoft but I haven't tried them yet.
Web hosting services from ICDSoft: Superior Tech Support and Super Fast Servers
Wazu also says they provide .jp web domains but I'm not sure where they are based (Australia?)
WAZU JAPAN Web Hosting
Did you also need an IP address in Japan? If this is important to you then you may need to go with a service based in Japan like the following but please note that the service prices are going to be more than other companies and will expect payment in Japanese currency:
Tsukaeru.net - Webhosting in Japan
Website Hosting Japan - Web Hosting & Domain Name Registration for Japanese Web Sites