The best way to get more chances at finding pet food in the rotation is to free up more slots and to ensure you are catching the rotations at the right time.
1. Craft all buildings that you can only have one of. The various pieces of the Chess Set, and Phoenix bases or other evolving building bases that come up. Keep them in inventory (unless you WANT to place them in your city), and they will not come up in the crafting options any more.
2. Make sure to check the crafting recipes on the schedule in which they turn over. You may need to spend diamonds once to adjust the time this changes so that you can check it the maximum number of times per day.
All this being said, it can still be hard to get enough pet food. That is why you may also have to come up with strategies to conserve pet food. Waiting until the second day of the tournament and getting in two rounds on one feeding is a good way. Also, if you have a Brown Bear, for example, I wait until I am very low on troops, then I feed and use timer instants to speed through troop production. If you only do this once in a while, you can really save on pet food.