The most famous souvenir from Tamagawa Onsen consists of a white powder which is recovered from the onsen once the water is evaporated. It consists mostly of inorganic salts and sulfur derivatives.
Japanese bring that home - or give it away as gift - and put it in their bath tub, thus recreating the onsen water at home and enjoying similar benefits...
You can check one of this "onsen flower" set sold at Akita Airport here : http://www.akita-airport.com/shop/goods01/029/029.html
The set looks like that (3rd picture from the top):
Years ago, many people were taking with them rocks that are found outside around the spring. Those rocks are slightly radioactive - it is still part of the onsen treatment - and are said to be a "cure" for persons with cancer. While there is strictly no medical evidence of that, it used to be really popular so that those stones were sold on the internet for ridiculously high prices... Now, it is forbidden to take out any rock of Tamagawa Onsen, which is in a protected area.
Still, go to http://auctions.yahoo.co.jp/
(which is the Japanese equivalent of ebay) and type 玉川温泉 - you will find many examples of stones to sell...
Hope this helps,