How to find a rental to move help one of MY current tenants move TO?

[Seth Nowak]

Is there a "concierge" apartment or rental house - finding service? 

I am house hacking and my upstairs tenant has a lease that doesn't end until August. Me and my partner are having a baby in July; her current lease ends in March. Our plan is to have her move in to my house. 

My upstairs tenant is willing to voluntarily move IF she can get accepted to a place that will accept her German shepherd and 2 cats and cost about $1200 per month or less, in Madison, WI. 

I've been online at apartments . com and craigslist and a few other sites searching for possibilities, but is SO time consuming! 

Who can I hire to find a place ASAP for my current tenant to move to? I'm open to any advice and ideas and solutions.