Well, it turns out at least one place still does: the Black River Historical Society! They have a nice selection, including their version of the classic 'Greetings' format shown above (in which they have craftily inserted the Moore House – their home) as well as others including one featuring the Lakeview Park Easter Basket.
The above postcard design is also available in their gift shop as a large jigsaw puzzle.
The coming weekend would be a great time to drop in at the BRHS. On Saturday, May 21st they are having a big 30th Anniversary Celebration. According to their website, the activities are from 1 pm until 6pm and include Trolley Tours for $1, a Scavenger Hunt, goodies for sale (popcorn, cotton candy, ice cream and soft drinks) as well as a "Through the Years" PowerPoint presentation.
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Incidentally, here's yet another "Greetings from Lorain" postcard variation that surfaced! It's a little on the generic side, though. And I'm a little skeptical that those are real Lorainites in that boat!