Facebook App do the followings:
1- post on Facebook custom post each Monday and Thursday
2- post on Facebook custom post with image each 13,14,15 of each Arabic month.
3- post on facebook custom post with image each Friday
4- ability to schedule more timings as required
like this app [url removed, login to view]
with admin scree to set all the above 4 options.
setup it and run it in Facebook App store for free, and have it post as our website having our brand and logo