Spanish term (edited): rincones itinerantes de lectura

I'm pretty sure the idea is that they will travel around the community with some kind of mobile library and set up spaces for people to read. None of the three options I gave above is actively used (except for mobile reading corner which was used once for an event in Singapore it seems), but I think they are understandable English.

If you wish to adapt the text more, you could use "mobile library". This term is actively used but usually in association with organized public libraries. Link here:

http://sussex.lib.de.us/libraries/sussex-county-mobile-libra...