I realize this topic hasn't been posted in for a little over a year now, but I thought I'd throw my experience in all the same. The game I'm currently running is in Aereth using Paizo's Pathfinder Rules (AKA 3.7). I'm using all DCC modules at this point, but only the first has been run "straight"; the rest have had to go through an adaptation phase to run smoothly For instance, the party is 5th to 6th level and are currently in the Temple of the Dragon Cult; there are nerfing rules provided, but they still need to be fine-tuned, especially with the 3.7 rules... I'm also planning on running a couple of 4ed modules, which will need to be more-or-less rewritten to work right.
Anyway, back to the topic. I have one player who really, really wanted to play a dragonborn - she had a dragonborn she really, really liked in our previous 4ed game before we ditched it in favor of 3.5/3.7 - but with the whole back story of the Dragon Kings it took a while to come up with a storyline justification for the existance of dragonborns.
What I came up with is this: my player's dragonborn is the *first* dragonborn... and he didn't choose to become dragonborn (which is the mechanism from the Races of the Dragon supplement), it was imposed on him around puberty (which retains some of the 3.5/3.7 mechanism of adding the dragonborn template to an existing character). This was done by the 3.5 Dragon-God pantheon.
In my storyline, the presence of the Dragon Kings and the Pool of Dreams is preventing the Dragon-gods from establishing themselves in Aereth - they have little to no influence as long as the presence of the Dragon Kings remains.
So, one of my campaign story arcs will take the PCs through DCC 30 and at the "completion" of the module (should they succeed, of course), the Dragon King's influence will finally be dissipated enough for the Dragon Pantheon to take hold in Aereth, and the dragonborn PC's "mission" will be complete. Then, of course, dragonborn characters could be made the "normal" way.
I just bring this up as a possible way to introduce dragonborns into other game: play you game on the assumtion that some hero somewhere along the way completed DCC 30, and the influence of the Dragon Kings has given way to the Dragon Pantheon. And dragonborns exist in the world accordingly.
I just realized that it's been so long since I've even looked at the 4ed rules that I may be wrong about the "story" behind the dragonborn race - my story line is based on the 3.5 Races of the Dragon "story"... but something along this line might work for 4ed dragonborns, too.
Just a thought