Every three weeks, MFZ releases a new bonus animal. You can get it with a purchase of 100 diamonds (around $10), or a pair for 200 diamonds. Sometimes there's a bonus NPC as well.
If you don't want to spend 100 diamonds, just wait! It will join the regular store eventually, and you'll be able to get it there. It will cost diamonds, but once it hits the store you can probably trade for it. Until it hits the store, there is no way at all to get it without buying at least 100 diamonds.
How long will I have to wait?
As of late 2016, the gap is an astonishing 15 months. The Maned Wolf was a diamond bonus animal in April of 2015, and made it to the store in July of 2016. No bonus animal has been released to the store since then. I'm not sure what's going on here - is MFZ planning something, or just tweaking to make it more tempting to buy diamond bonuses? The gap used to be a mere six months.