Yes, thats absolutely possible. Are you on a Cpanel Server?, if yes you can set default nameservers different for different resellers.
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You just need to create necessary A record for your nameservers (i.e. A record for ns1 and ns2) and then you just need to register your private nameservers from your registrar. You will need to specify nameserver and its IP address while registering them from your registrar.
Once the nameservers are registered successfully, you can use them.