So basically... look at all the fan-made stuff that's selling, and try to get a piece of that pie. I wholly agree. I'm actually probably about the least inclined to buy a t-shirt as opposed to just about any other LoL/Riot branded everyday item. I'm a big tea drinker (and yordle fan) - how about a mug set featuring each yordle on a mug?
They tried to host their store themselves a while back. I don't think there was anything wrong with the store itself, but the choices were so limited that I think it floundered and they ended up dropping it and outsourced that job to Jinx. But it still feels like Riot has done nothing to maintain even that. There hasn't been anything new on there in a while. Some of the more popular items are sold out and haven't restocked. Their official Teemo hat is gone, leaving players to have to seek out similar products made by fans of the game instead.
Heck, a couple years back, Riot even stated that they were working on a Teemo plush (and that it was specifically Astronaut Teemo). People have clamored for a Koggy plush. I'm guessing the Teemo plush was shelved when the store wasn't doing as well as Riot had hoped.
I've got an idea that would make the whole deal even sweeter, too, but it would probably require Riot to go back to operating the store themselves. Why not have a reward system for purchases from their store? Either have a point system for those purchases, where points can then be used to either get discounts on other items in the store, or maybe even be traded in for an amount of RP on your account. If they didn't want to do it that way, they could even reward your account with RP for each purchase, based on a percentage of what you spent in the store.