You can setup a private network between the two servers only if they have additional NICs that are connected to each other (directly or via a Switch etc). You can do all of this through the Network Connections GUI but if you want to do it from the command line you can get it all done via the Netsh command. Be sure to start this from an elevated command prompt if you are on Windows 2008.
netsh interface show interface
That will list all available adapters. If you have more than one physical (wired) NIC they will show up as LAN Connection 1, 2 etc.
Admin State State Type Interface Name
Enabled Connected Dedicated Local Area Connection
Enabled Connected Dedicated Local Area Connection 1
This shows a system with two LAN adapters that are detecting that they are connected to something. If you don't have a second adapter you can't set up a completely private network between your servers and if the second adapter is listed as disconnected you will probably need to get someone to resolve that by visiting the servers to plug in some cables.
You can list the current address and other configuration data for the interfaces with the show config command so you can be certain which interfaces are available for you to use, and in which way.
netsh interface ipv4 show config
ipconfig /all will give you pretty much the same info (and covers ipv6 at the same time).
You can set the ipv4 address on an unconfigured interface as follows.
netsh interface ipv4 set address "Local Area Connection 1" static 192.168.1.10 255.255.255.0 192.168.1.1 1
The parameters after "static" are ip-address, netmask, gateway and gateway metric. Be careful that you are not selecting the primary interface of your server with that as you will almost certainly lose connectivity if you execute that on a remote system with your primary interface selected.
You can also add additional ipv4 addresses to an existing NIC provided it is not already configured for DHCP. This option is almost certain to work for you as it is what your provider described as adding an "aliased ip".
netsh interface ipv4 add address "Local Area Connection 1" static 192.168.2.10 255.255.255.0
Given that you will already have a default gateway you can leave out the gateway options.