I have done some more reading:
http://eh.net/encyclopedia/article/frank.international.rubber.marketIt is rather close to the time when rubber started to be produced in industrial quantity. It started in the 1870s in Brazil. British rubber production in Southeast Asia started in 1888. I reckon it could well be a slingshot/catapult now.
I was previously going off the date for the introduction of pneumatic tyres which didnt begin production until 1890.
I wonder what rubber products were first turned into catty bands, if it wasnt inner tubes?
[EDIT]
The rubber band was patented and manufactured in 1845:
http://www.therubberband.info/history.php Athens-Clarke County Georgia: Sec. 3-5-16. Slingshots. No person shall use for amusement or otherwise any Alabama slingshot or any slingshot or similar thing in the urban service district. (Ord. of 4-7-92, § 8)
http://www.dumblaws.com/laws/united-states/georgia?page=20