Is it possible to get Cartel Coins from any other source?

Solution 1:

Yes! In Game Update 2.0, certain Legacy Achievements grant Cartel Coins. They only grant once per Legacy, so it's not a feasible way to get a lot of them for free, but it's kind of cool.

From the official SWTOR blog (emphasis mine):

This update also includes an all-new Achievements system. Starting in Game Update 2.0, players will be able to earn Achievements for all sorts of activities in-game, including crafting, exploring and unleashing their wrath on the world around them. Over 1,900 Achievements are in this release, and we see the system as a great way to add more, and more varied gameplay in future updates. Achievements can also grant rewards such as titles and in some cases Cartel Coins.

Currently you can get a total of 860, as per Dulfy.

Solution 2:

To the best of my knowledge, No. However, most (all?) items and upgrades purchasable with Cartel Coins are themselves tradable and can be resold using in game currency, such as via the GTN.

Solution 3:

This may not have been the case at the time. But it appears bioware/EA have partnered with amazon as they sell cartel coin codes which come with a free gift (read : cosmetic/noncombat companion).

Source- http://www.amazon.com/Star-Wars-The-Old-Republic/dp/B00DIIZ15A