Actually, it is possible to have 5 units per barracks. 4 in the normal slots, then 1 premium slot. You can get free diamonds by completing certain quests, or winning competitions on the forums, but the best way is to 'Earn' them. Click the '+' next to the diamond icon in the top-right of your game screen. In the pop-up window there should be a button 'Earn my diamonds', follow that and then you should see a range of offers for free diamonds, such as surveys, signing up to trials etc.
Without diamonds, if you want more than 4, you need multiple barracks. (Even with diamonds you can only have 5 without bulding more barracks.)