I'm sure some do, but I think script installers are more popular. They are typically plugins for popular control panels. They add a page or pages to the control panel from which you can easily install and uninstall a wide variety of scripts, including popular CMSs.
They ask a few questions and do most of the hard work.
Any host that uses Cpanel with Fantastico included. There are a kazillion of them out there. But you still have to know how to back up your database in case you have any problem or have to change hosting.
I'd just ask the potential new host if they can install it for you if you sign up with them. 90% will just say sure and stick it on there FOC. Always ask for something when you get a new host... more space, a bit more bandwidth, an extra database... it's rare to find a host who won't stretch their package a little for you.