The folks told me at Delancey told me not long ago that the Padron season was closing. We have to be close to the end. However I see that they are on the menu at The Walrus and the Carpenter in Ballard. You might want to give a quick call over there and ask where they are picking them up.
I thought that Delancey's uses Billy's for a lot of their produce. http://www.billysgardens.com/index.html and read about a few references to Billy's Padron chiles on the web. See http://mixedgreensblog.com/2009/09/30/seasons-eatings/whats-hot-roasted-peppers/ and http://blogs.seattleweekly.com/voracious/2010/03/ask_the_critic_redux_green_chi.php
However I don't see Padron chiles on Billy's list of produce.
I was reading recent posts for both Wallingford and Ballard farmer's markets indicating that Alvarez Organic Farms has a ton of hot pepper available ... apparently they grow over 100 varieties.
This article mentions that they were selling padron chiles a couple months ago
1415 NW 70th St, Seattle, WA 98117
I've purchased some peppers from some vendor at Columbia City that seems to specialize in them and sells many varieties. Though they were labeled as "padron", they were actually much hotter than real padrons, and I think they have been misidentified. But this vendor also sells shishitos which are a good substitute.
Which farmers markets did you check out? The last time I was at the Broadway Sunday Farmers Market on Capital Hill there was a wide variety of peppers, many more types then the other farmers markets in the area. I don't remember which vender it was specifically, but there are only a few that list peppers on the site.