Actually I disagree with Uco about the commonness of cycling even with children in Tokyo. It however depends on you and how used you are to cycle around in a busy city.
In Japan however you are generally allowed to cycle on sidewalks and while I personally don't like it, with a child (and without) it is very common and safe, but slow.
Consider that there are few and badly interconnected cycle paths, BUT there are many backstreets, even in central Tokyo, with little traffic.
Now to your question for bicycle rental. This might actually not be trivial. Try to reach out to these guys:
http://freewheeling.jp/ they offer cycle tours and have rental bicycle for them. Maybe they can also long term rent you a bicycle. Or maybe they know someone who knows...
I think there are also other people offering bicycle tours in Tokyo. So just try to reach out to them too.
Here some more information on bicycling in Tokyo:
http://www.tokyobybike.com/2015/08/why-suburban-tokyo-is-teeming-with....He has also other articles, a bit outdated maybe, on bicycle rental.
http://www.tokyobybike.com/2015/01/where-can-i-rent-bicycle-in-tokyo.h... According to this you might be able to rent a cycle with child seat in Setagaya.
http://www.city.setagaya.lg.jp/kurashi/107/165/831/d00005236.htmlThey seem to have cycles with children seat. "チャイルドシート付自転車"
There is a list with cycle rental spots close to train stations in Setagaya. Before getting too exited, please review the page in detail. Maybe Uco could help you? I am not sure if as a tourist you can rent and if multiple day rentals are okay.
And just in case you are in Tokyo on the 3rd Saturday of a month, why not join up with this crowd of mixed Japanese and foreigners riding through Tokyo at night. It's for free and great fun:
http://nightpedalcruising.com/ Enjoy your trip to Japan!
PS: If you are interested in following me on my trip around Japan on a brompton, I will restart next week😊
https://bicycletraveljapan.blogspot.de/?m=1