We have two different active directory domains. Is it possible to have to SQL Server 2008 instances running on the same machine and have each instance tie to a separate domain?
No, because it's the server that is joined to a domain or to another one, not the applications running on it; and a server can be joined only to one domain at a time.
The only way to achieve this with only one physical server is by hosting two virtual machines on it, each one joined to its domain.
Another possible solution, if the two domains are in a trust relationship, would be having the server joined to one of them and assigning permissions to users of the other domain on one of the two SQL Server instances; but this would require a trust relationship between the two domains, and would not provide the same level of security and isolation.