There is a conflict in your question, you have 1 VDS but want to have 2 hosts, ns1 & ns2, as DNS servers. You'll need two VDS if you want 2 hosts, best practice would be for the 2 hosts to be on separate physical machines in different geographic areas and networks.
Also, you don't need your own name servers to host on the VDS, you can use GoDaddy DNS and just set the records to point to the correct host. Since a DNS failure or misconfiguration will stop all traffic to the sites make sure you have good backups and understand how it works before you proceed. If you still want to try it:
Get a public, static IP for your server.
On your OS of choice, install your DNS server of choice.
Configure the primary zone Domain.com in the DNS server.
Add the A record ns1.domain with your public IP.
Add a CNAME for www.domain.com to point to ns1.domain.com
Add an MX record(s) for wherever you can receive mail for domain.com.
In GoDaddy DNS config, set it to "Use Other DNS servers", enter ns1.domain.com for the first DNS server.
Allow pings to ns1 for testing.
Confirm that the zone/hosts are configured correctly by using digg/nslookup/ping to test.
Resolve errors.
Find another host to be ns2.domain.com with static IP.
On ns1, add an A record for ns2.domain.com.
On ns1, configure DNS server to allow ns2 to receive updates for each zone.
In GoDaddy DNS config, "Use Other DNS servers", enter ns2.domain.com for the second DNS server.
On ns2, in the DNS server, add a secondary zone for domain1.com, point to ns1 as the primary.
Confirm that the zone transfers correctly by using digg/nslookup/ping to test.
Resolve any errors.
For the other domains:
On ns1, add a primary zone for domain2.com in the DNS server.
Add an A record for www, and CNAMES for anything else you need on that host.
Add an MX record(s) for wherever you can receive mail for domain.com.
In GoDaddy DNS config, set it to "Use Other DNS servers", enter ns1.domain.com for the first DNS server.
Confirm that the zone/hosts are configured correctly by using digg/nslookup/ping to test.
Resolve errors.
Repeat for each domain.
On ns2, in the DNS server, add a secondary zone for each domain above, point to ns1 as the primary.
Confirm that the zone transfers correctly by using digg/nslookup/ping to test.
Resolve any errors.
Repeat.
Disable ping on ns1 and ns2 as you prefer.
Document, create offsite backups of ns1.
Make all future changes on ns1.