To that end, I've compiled a few suggestions for minimizing the amount of time you'll have to spend gathering coins and hunting for burdens.
The timeless chests are the easiest way to accumulate a few thousand coins and, perhaps get a burden or two. The Blazing Chest has the highest chance of dropping a burden, and is usually well worth the travel. However, different types of chests can be looted at different times. Some can only be looted once per character, while others are once per week.
I found a great guide that details where each treasure chest on the Timeless Isle is at, and what type they are. It can be found by going in the MMO-Champion forums here. I would recommend looking through it to see what possible chests you might have missed.
Doing the quests on the Timeless Isle should net you 1,000 coins from the daily quest and another 3,000 for the weekly ones, so killing your 20 elites and 5 rares, as well as collecting 50 epoch stones can add up over time. However, once the quests are completed and you still need Timeless Coins it becomes all about the rare hunting.
Rares, particularly the rares with a set health pool (doesn't increase as more people attack it), are the best way to get burdens and coins. However, the more rares you defeat, the less they drop, so its really important to tag the best ones. I would recommend Evermaw, Vazuvius, Yuolon, and Cinderfall as priority targets.
If you would like to find a detailed guide on where each rare spawns and other possible drops you should take a look at the WoW Rare Spawns Blog, written by Euphyley. It was written to enable people to get the Timeless Champion achievement (achievement for killing all of the Timeless Isle rares) but the locations are useful for those who needs coins and burdens as well.
Finally, there is a addon known as Rare Coordinator which you can use to help identify what rares are currently alive and how long its been since they died by communicating with others on the Timeless Isle with the same addon. It can be downloaded through Curse using the link.