Is there a website or something for this service? My only concern is for the trip back to the airport and if they can get it there in time. We would send it on Sunday so I don't know if they work that day.


No need for a website. Any hotel can arrange this, and reservations are unnecessary.

It would be helpful to the hotel staff, however, if you could print out the Japanese-language web page of your Kyoto hotel, so that they can copy its address correctly in Japanese script. (Place names are especially likely to be spelled with odd combinations of kanji.)

On my 2013 trip, I somehow managed to arrive on a day when all the affordable hotels in Tokyo were full, so I spent the first night in the town of Narita. It was a Sunday morning when I made the trip into Tokyo for the beginning of a 12-day stay, and the hotel had no trouble shipping my luggage.

Government offices and services (e.g. the post office), banks, corporate offices, and schools are closed on Sundays, but stores, restaurants, and other commercial and retail service outlets, as well as museums, operate as usual. Sunday is a major shopping and excursion day in Japan.