Also, NEVER try for the jackpot in the fan gifts. It's a total scam.

diamonds are hard to get, for sure.
Some Tips: 1. The London mansion has a maid, that will give you 1 diamond a day. 2. diamonds drop randomly from movies, or interacting with items. Check in throughout the day and use your energy to just click stuff. 3. If you don't log in for about 3 days, you'll get a "lucky hour" in the casino, where the prizes are amazing. The best game is the slot machine for 3 diamonds a spin.
Lastly, it's not fair, but you basically need to spend $5 to get the "seed money" diamonds to parlay them into some serious stockpile. Watch and wait for the specials. Each day, the special will include more and more diamonds, until it resets back to crap. The max diamonds you can purchase for the $5 is about 500. When you see that offer, buy it, then log out for 3 days and use that lucky hour to get, literally, thousands fo diamonds.
Hope this helps!