The Ethernet library that OpenSprinkler uses does allow defining custom DNS when using static IP. Unfortunately this is currently not exposed in the firmware / UI. When using static IP, it assumes the router is the DNS server, which is not an ideal solution in some cases.
That’s why we recommend keeping OpenSprinkler in DHCP mode (so that the router will automatically populate the correct DNS IP to the device). You can still achieve static IP by using your router’s DHCP reservation / IP reservation feature. This way, every time OpenSprinkler restarts and requests DHCP, the router will always assign the same IP to it. Unless if the router doesn’t support DHCP reservation, there is really no need to set OpenSprinkler in static IP mode.