How do you get Diamonds and more stables.... I need to buy another stable and hatchery but I need diamonds first and I don't know how to get any. Is there any other way to get more stables and hatcherys without diamonds?

You get diamonds from the Diamond Shop which you buy with real money. You can alternatively get diamonds from the Currency Exchange, you buy those diamonds with gold from other players.

Taking a look at your stables though it looks like you just need to buy tabs first. You buy tabs with gold, stables can have up to 8 tabs...after that you will need to purchase a new stable. So just go to your stable page and click on the 'Purchase Tab' button to get more tabs. As for the hatchery, hatcheries are currently not limited in space. So you do not need to purchase additional space for your hatchery.

Thanks.