The answer to you're question is no, the trainer will not have more freebie recipies for you to learn. That doesn't mean that there aren't more "easy" to get patterns.
Here's an example of an easy pattern to get. What you'll want to do is a little faction exploring. Try looking up the faction reputation rewards for the various races around BC. This is just one of many examples. The constortium is relitively easy to gain rep with. Just head to nagrand and grind out some of those really big void walkers. The items they drop (shadow motes) sell well enough on Crushridge, and I think as a leatherworker you may even use them in your craft later. May as well start the grind for your mats now while earning some nummy faction.
I hope this helped.