I have my main home network with a Fritzbox on 192.168.1.0/24 using ISP supplied DNS with a subnet mask 255.255.255.0. I would like to add a D-Link DIR615 which gives out IP addresses on the 192.168.0.0/24 network using a different internet based DNS server (eg CloudFlare's 188.8.131.52 or Google's 184.108.40.206) but routes via the Fritzbox as the gateway. I also have a Linksys 54GL which can run DD-WRT or similar, which tends to be pretty flexible.
When I set up the D-Link as 192.168.0.1 and told it to use the Fritzbox gateway 192.168.1.1 it told me I couldn't use a gateway on another network.
Update: all I really want is devices connected to this new WAP to use a different DNS server.