Instagram does not offer APIs to schedule a post for future. However, we have found a way to do so. Not only scheduling but you can automate things like liking, commenting or even copying followers of your competitors. Give it a look at http://fanharvest.com/
It is in private beta at http://folwd.com/vipbeta.
Folwd (pronounced followed) recommends awesome content tailored to your audience and then automatically (or after approval) shares it on your social accounts. It is like hootsuite/buffer with daily recommendation engine.