Add users from other domain

Hello,

We have 2 domains in our infrastructure (say D1 and D2). D1 and D2 are independent domains, we cannot enable trust between these domains. Machine M1 is in domain D1.  

For a business reason, we want to add a user of D2 domain to the machine M1.

The issue is :

When I try to add the user, try to look up the user, the locations list for user lookup does not list the D2 domain. So, I am unable to add the user. 

Can anyone suggest how I can solve this issue?  Any pointers will also help.

Regards

Sh