With Team Pages, you unfortunately cannot create One-on-One events. There is a quick workaround you can do to achieve the same goal. 

If you create a Collective Event, but only add the desired user that is to be included, the Collective event will pretty much work just like a One-on-One but still be visible on Team Pages and the Team Landing Page. 

I have the same problem thanks to you now my problem is solved. 

FYI - this topic that my colleague, Sam, wrote goes into detail about how to accomplish this! I hope this helps!