Am I understanding correctely: Your Server IPs are dynamically changing on each reboot?
If so, you could enter a reservation inside your DHCP-Server for the MAC-Address of your Server - please note that is always better to assign a static IP-Address (especially when the DHCP-Server is running on the same device, as the DHCP-Role is started a way after the networking).
To manually change / set an specific IP-Address to IIS-Service:
Open the IIS-Manager and navigate to the site you want to bind a different IP-Address to and do a right click. Now choose "Bindings". You can now either edit the existing entry and change the IP or add a new entry.
Please note that you have to add a second IP-Adress to your network adapter (in case you don't have more than one network adapter connect with an IP)
RAS: As far as I know you cannot change IP Bindings on Routing and RAS - if you have more than one network adapter you can choose the used adapter instead (which would "change" the IP used).
Hope that helps at least a bit.