Oh man, there is a chain store there called "Petersen Medical" that I used to get Molicare Superplus diapers. They carried them right on the shelf. I am not sure if they still carry them or not, but it's worth a look. You may find some other brand there that you'd like to try anyway.
Honestly I don't think there's any good places to buy high quality diapers in Northern Utah. I'm living in Logan right now and I ended up just ordering some online because I couldn't find any place that had any. If you can have them shipped to you I think that would be the best option. Plus most suppliers have discreet shipping, so the boxes are unmarked. Good luck though.
And if you find anywhere that does sell them, please tell me!