In the Pathfinder campaign setting, there are no big racial pantheons. There are some racial deities, i.e. gods and goddesses that are almost exclusively worshipped by one race, but that's not really the norm.
The races don't usually stick to "their" deities, either. And some of the "racial" deities even made it big. Torag is a dwarf deity, and Calistria is elven, but both are worshipped by lots of people all over the Inner Sea Region.
There is one deity that is of gnome origin, but in that case, gnome isn't the whole truth: Nivi Rhombodazzle (The Gray Polychrome) is a goddess of the deep gnomes - they say she was the first ever deep gnome.
Gnomes were usually fey creatures from the first world, and deity worship is basically non-existent there. They did adjust to many things when they came to Golarion and became humanoids, but they didn't create gods for themselves, and no gods showed up to be theirs, either.
Those that do worship someone, Cayden Cailean, Desna, Shelyn, Nethys, Torag and Erastil are among the more common choices. I'd guess Calistria, as a hedonist, will also appeal to many gnomes.
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Of the First World dieties, the Eldest, the Lantern King (CN, power of laughter, mischief and transformation, domains - charm, chaos, madness, trickery, favored weapon - dagger) seems like a natural fit for many gnomes. (a tiny bit more info on him is available in the Inner Sea World Guide, p 233-234, and a tiny bit more in Kingmaker 6 (AP 36) p. 68, but in both cases, I'm talking a couple or three sentences, so don't feel compelled to buy a $20 or $50 book just for more info on the Lantern King!).
The transformation aspect fits well with an alchemist, in particular.
The fun aspect of a diety that is so sparsely detailed is that you can make up tenets of faith without fear of contradiction. :)
The Lantern King, portrayed as a will-o-wisp like entity (although he laughs at the notion that he is the creator / father of that race) is described as being reknowned for his whimsical and capricious nature, even by fey First World standards (no mean feat!), so it sounds like you'd be at liberty to make up fairly nonsensical observances and acts of faith.
I'd also take a look at the Pathfinder Wiki's religion/deities portal. There is actually one distinctly gnomish deity, Nivi Rhombodazzle, who is briefly featured in both Gods and Magic and the newer Faiths of Purity. Emphasis on brief.
Sivannah, Brigh, and Gozreh/Green Faith are also mentioned as being worshipped by Gnomes in the "Gnomes of Golarion" Companion book, along with some of the other aforementioned deities.