wireless router > vonage router

mdtiger,

Yes, you can connect the routers in "series," but need to be careful.  You cannot connect the two routers to the modem, even if you use a switch, since they both need IP addresses and normally ISPs only allow one per modem.

If your intent is to use the Vonage router only for its telephone port(s), then simply connect its WAN port to one of the existing router's LAN ports using a straight through ethernet cable.  Then plug in the phone.

If you intend to use each router for PCs also, then you need to decide if you want two subnets or one.  For two subnets, each router represents a subnet and depending on the brand of the existing router you may need to change the private IP address range in one of the routers so there is no duplication.  Give the second router a static WAN IP address in the subnet of the first router.  Then place that address in the DMZ of the first router.  With two subnets, the PCs connected to one router will not be able to perform File and Printer Sharing with PC connected to the other router.

For one subnet, I suggest you connect the Vonage router first and then configure the existing router as an access point, turn off its DHCP server and just run it as a "dumb" switch.  With one subnet all PCs will be able to File and Printer Share.

mdtiger,

Configure the Vonage router with a static WAN IP address in the range of the existing router.  In the existing router either configure the DMZ to forward to the Vonage router or do the port forwarding as documented here.