We regret to say that the PS4 Mods Beta for Fallout 4 has been delayed. We will update everyone when we can.— BethesdaGameStudios (@BethesdaStudios) June 29, 2016
It's not the first time Bethesda's had issues with its games on PlayStation consoles, especially on PS3. People hoped that the move to PS4 which change this, however thanks to a few issues the developer was trying to fix with mods, such as the file size limit of 900MB, compared to the 2GB limit on Xbox One, the decision seems to have been made to delay the release for now.
Hopefully we'll get a release eventually.