COE for Dependent

A friend of mine (newly wed) is in Tokyo right now on a Tourist visa. The visa expires in a month and 10 days. For some official reasons they've not been able to apply for the COE so far. But are planning to apply in a day or two as soon as the matters get cleared. She's applying for a dependent Visa. Considering the fact that her husband has been in Japan for about 6 years on a COE Engineer Visa, how long will it take (approximately) for her COE to come thru? Will she have to go to her home country to finish the procedure? Neither of them is a Japanese National.
Any suggestion or advise to speed up the process is appreciated. Thanx in advance.

A COE is a Certificate of Eligibility, so there's no such thing as a COE Visa, a COE helps get a Visa.

To answer a few questions, will she have to leave Japan? Well it depends if the COE is processed fast enough she might be able to change it in Japan, but if its only a month left, thats cutting it close, as COEs can take UP to three months to process. So if she doesn't get it on time she doesn't neccessarily have to go to her home country, she might ask for an extention of her current "Tourist visa" or if she is a visa waiver ask for an extention while her COE is being processed, but this all really depends on nationality, and if 90 days is up and she can't get an extention and still waiting for the coe to process, then she would have to Leave Japan, doesn't have to be home, just has to be out of Japan to finish the work.

Thanks for the rest of the information. Did some study myself and cleared the doubt about the COE to get the Visa.
Will anyway contact the immigration office soon to start the process.