Instagram has FINALLY listened to the plight of social media managers and has begun to allow businesses to scheduled content for the platform.
Unfortunately, this functionality is only available via their API, meaning that we have to rely on third-party programs like Hootsuite or SproutSocial for the time being. But it's better than nothing.
At the time of this writing, it appears that only Hootsuite has already implemented the API, but I'm sure your preferred content management system will be fully equipped in no time.
We're not there yet, but progress is progress.