Any DNS expert here? Need help [URGENT]: Intranet NameServer for Public Domain

I have registered a domain name domain.co and have a intranet DNS server (BIND) which is serving the queries. I wanted to add glue-records to my private ns, but it turns out that .co registry doesnt support private ips as nameservers. As per my register :

The error message you encounter while trying to create child name server is because .co registry is not accepting the IP address: 10.10.0.1

I have another domain example.com where I have added A records pointing ns1.example.com -> 10.10.0.1 and ns2.example.com -> 10.11.0.1

Now I have changed the name servers of domain.co (to ns1.example.com , ns2.example.com)

But when I try to resolve the domain name I get server fault. [Note: the DNS have propagated already]

$ dig stage.domain.co

; <<>> DiG 9.9.5-3-Ubuntu <<>> stage.domain.co

;; global options: +cmd

;; connection timed out; no servers could be reached

But dig stage.domain.co @ns1.example.com returns properly.

$ dig stage.domain.co @ns1.example.com

; <<>> DiG 9.9.5-3-Ubuntu <<>> stage.domain.co @ns1.example.com

;; global options: +cmd

;; Got answer:

;; ->>HEADER<<- opcode: QUERY, status: NOERROR, id: 17613

;; flags: qr aa rd ra; QUERY: 1, ANSWER: 1, AUTHORITY: 4, ADDITIONAL: 3

;; OPT PSEUDOSECTION:

; EDNS: version: 0, flags:; udp: 4096

;; QUESTION SECTION:

;stage.domain.co.       IN  A

;; ANSWER SECTION:

stage.domain.co.    86400   IN  A   10.11.8.35

I have tried a lot but couldnt get any help regarding this. I want to achieve this so that I do not have to edit /etc/resolv.conf to point to my internal dns, since I want to spawn machines at run time which are inside my network and I want dns to be resolvable directly.

Why does it throws server-fault when directly querying for the domain name? Is it because its intranet ip ? I want those to be resolvable to my intranet machines only.

Please help! 

THIS IS URGENT.