Are private IP addresses available for VPS to VPS communication?

Short Answer

Yes

Long Answer

VPS' belonging to the same account are grouped into the same private VLAN. As such, you may assign any RFC 1918 private address to your interfaces. They will not conflict with any other customer.

Additionally, since the VPS' belong to the same private VLAN, using private addresses for VPS to VPS communication is not necessary. In fact, you can communicate between VPS' using their public IPs and since the traffic will not leave your VLAN, you will not be billed for the traffic.