There isn't an Android permission that will allow it. One thing you can do is write to Google, explain what your App does and why it needs to be able to SMS directly. If they think your App is worth while for the task, they may indeed allow it.
If Google don't want to play (pun intended), there are other stores that may not have such restrictions, or you could set-up your own store on your own website.
https://www.professorcad.co.uk/appinventortips#TipsAppStores