Amazon Appstore, Getjar, SlideMe. However, is it that the app didn't work or is it that the Play Store wouldn't let you download it? Perhaps telling us what the app is and posting your tablet's make and model can give us some insights.
It's just a Clu by Curtis? I bought it for $100.00 at Big Lots. I've learned from experience that tablets without the Google Play Store have .apk install issues. An .apk might install but won't run properly or won't even install. Typical Linux. I wish I'd spent the extra money and bought an iPad Mini or MS Surface. These Android devices are kind of limited.