Installing a service remotely requires no privileges on the target machine except the right to log on. But the account used must have the SC_MANAGER_CREATE_SERVICE access right on the Service Control Manager on the machine. This right is by default only given to members of the Administrators group. So by default the installing account must be an administrator on the target machine.
For systems prior to Windows Server 2003 SP1 (i.e W2K3, XP, W2K, etc.) the SCM security descriptor cannot be altered so this is the end of the story - you must be an administrator to install a service.
For W2K3 SP1 and later, if you do not want to run the script as an administrator then you could modify the security descriptor on the Service Control Manager for the target machine to include an ACE for the account the script runs under with the appropriate right(s). In general though, you would probably be better off re-thinking your deployment process to use an administrative account for service installation.