Try adding "gem install json" before "gem install librarian-puppet" in the file {vagrant path}/puphpet/shell/librarian-puppet-vagrant.sh (probably somewhere around line 72)
I was having a similar issue and found the above solution at https://github.com/puphpet/puphpet/issues/455. My issue had nothing to do with the proxy stuff mentioned there, however the json errors were similar to mine. Seems to work for me.