Good news! Wix has implemented a chat function among members that functions like private messaging.
To open a chat discussion, go to the bottom of the page, in the lower right-hand corner. You'll see a box (currently colored gold) that says Members Chat. If you want to send someone a private message, click on the arrow pointing upwards. You'll get the option to chat with other members of the site.
If you have any questions about this function, please let me know, either by responding in this thread or by sending me a private message (that is, if you can figure out how to do it).