Errors encoutered:

Error: iptables v1.3.5: can't initialize iptables table `nat':
 ipt_state/xt_state...FAILED [FATAL Error: iptables: 

You must login to your root node and enabled these modules first:

modprobe iptables_module
modprobe ipt_helper
modprobe ipt_REDIRECT
modprobe ipt_TCPMSS
modprobe ipt_LOG
modprobe ipt_TOS
modprobe iptable_nat
modprobe ipt_length
modprobe ipt_tcpmss
modprobe iptable_mangle
modprobe ipt_tos
modprobe iptable_filter
modprobe ipt_helper
modprobe ipt_tos
modprobe ipt_ttl
modprobe ipt_SAME
modprobe ipt_REJECT
modprobe ipt_helper
modprobe ipt_owner
modprobe ip_tables
modprobe ipt_MASQUERADE
modprobe ipt_multiport
modprobe xt_multiport
modprobe ipt_state
modprobe xt_state
modprobe ipt_limit
modprobe xt_limit
modprobe ipt_recent
modprobe xt_connlimit
modprobe ipt_owner
modprobe xt_owner

Then stop your container from the main node, with the following command (change number 100 with your VPS id):

vzctl 100 stop

Next execute the following command to enable the modules for your VPS on startup (again replace 100 with your VPS id):

# vzctl set 100 --iptables ipt_REJECT --iptables ipt_tos --iptables ipt_TOS --iptables ipt_LOG --iptables ip_conntrack --iptables ipt_limit --iptables ipt_multiport --iptables iptable_filter --iptables iptable_mangle --iptables ipt_TCPMSS --iptables ipt_tcpmss --iptables ipt_ttl --iptables ipt_length --iptables ipt_state --iptables iptable_nat --iptables ip_nat_ftp --save

Then finally restart your VPS:

vzctl 100 restart

If this still does not work, you may have to update IPTables on your CentOS 5.9 (just a guess, as IPTables 1.3.5 comes with this version of centos):

tar xjvf iptables-1.4.20.tar.bz2
cd ./iptables-1.4.20
make install
service csf restart

This should hopefully help you fix those CSF errors!