You can't install software "to a domain", because a domain is a concept, not a machine. I assume you mean "to all machines in the domain" ? Or more probably, "Most of the machines in the domain, because I don't want to push MS Office to my domain controllers."
Yes, this can be done with a GPO. Make an OU (or more than one) that contains all of the machines you want the software on, and then assign the software to the OUs. You can also assign software to users, or even publish it to users, but that requires user interaction, which you ruled out.
When you've done whatever you need, you can remove it. Instructions here: http://support.microsoft.com/kb/816102
There are plenty of other possibilities. Your software may come in a very easy-to-use MSI that you could install remotely using a script that loops through every machine in your domain and pushes it via psexec. You'd have to test this.
You can also buy plenty of commercial software that will let you do things like this. Since you didn't give a budget, I assume you want to do this for $0.00, but there's stuff out there. There's also open source packages that you could play with.