I used to go at Mc Party (ballon-müller) at the rue Simon-Durant 7 in the Acacias area. 

http://www.mcparty.ch/our-stores

just an update, there's a possibility they are called now *La bamboula* but I think you'll find some stuff there

rue de la Rotisserie 13: http://www.lagaite.ch/

Have you tried King Jouet.  There is one in Carouge on Avenue Cardinal-Mermillod.  I think there is also one in Meyrin.  Check out their website http://www.king-jouet.ch/

Coop City also has some nice supplies.  Located in Bel-Air Cite and Plainplais.

Go to http://www.mcparty.ch/our-stores, as Bertrand said. They are the cheapest and have the biggest variety. Their store is in Carouge. 

You dont need to get things from your city.  This is the era of online market and you can easily get thing of your choice online.

I  want to share a link with you where you can have that kind of party supplies online. http://www.windycitynovelties.com/758c/graduation-paper-goods.html

I think this is more more relevant link.