I don't know of any long-term storage like that. There are plenty of luggage courier services at the airport who would be able to courier your suitcase anywhere in Japan for around $20USD. I'd just courier it to your relatives. You can either pick it up from them when you leave, or they can take it to any convenience store and get it sent to the airport for you.
EDIT: I did some digging around and GPA offers baggage storage in both terminals. Their rates are pretty reasonable, too.
Small Baggage: 310 yen / day
General Baggage: 520 yen / day
Large Baggage: 820 yen / day
They'll store your bags in their luggage room for up to 30 days.
Whoops, I didn't notice that I wasn't logged in when I made that edit.