No, the men of Dale aren't of Numernorian stock. They're descended from the Northmen of Rhovanion, the northern... realm ("kingdom" is too organized a term) that ran from the Misty Mountains in the west all the way to the sea of Rhûn in the east, thus covering most of the area of the latter half of the Hobbit, including Mirkwood, the Lonely Mountain and, yes, Dale.
These ancestors of the Dale-men are the same horse-folk who, hundreds of years before, rode south to the aid of Gondor and founded the kingdom of Rohan. Also among these lineages in Vidugavia, the self-proclaimed King of Rhovanion, whose daughter married the King of Gondor, and event which led to the Kinstrife, a messy piece of Gondorian history. It's possible that Bard, through Girion of Dale, can trace his lineage to Vidugavia, but this isn't well established.
It's not well documented who exactly these men are and how they came to Rhovanion originally, as far as I know. While the Numenorians are Men who came into Beleriand in the first age and fought in her wars alongside the elves, it's likely that the Northmen of Rhovanion, many miles to the east of where Beleriand sank, were tribes of men who never made it there, and never came under the influence of the elves, or else men who fled Beleriand during its final wars, or an intermingling of the two. There were quite a few such tribes mentioned in various writings.
Here is a quote from The Lord Of The Rings, spoken by Faramir to Frodo when he captured the hobbits outside Mordor, speaking of the Rohirrim and suggesting (though not confirming, since his knowledge is admittedly limited) that the Northmen, ancestors of the Rohirrim (and thus of the Dalelings) are related to the Men of Beleriand who would later become the Numenorians, though a different offshoot of their stock.
Indeed it is said by our lore-masters that they have from of old this affinity with us that they are come from those same Three Houses of Men as were the Númenoreans in their beginning not from Hador the Goldenhaired, the Elf-friend, maybe, yet from such of his sons and people as went not over Sea into the West, refusing the call.
(The Lord of the Rings, Book IV, ch.5 The Window on the West)