If you have one old Wii connected to watch Netflix you will have to find an alternative as Netflix stops it support on 31 January 2019.
Netflix already sends emails to his clients with a relevant announcement, to them warns that Nintendo will "suspend" Netflix and other streaming video services for the Wii after January 31st, 2019. The shutdown will come alongside the closure of the Wii Shop channel, and essentially the console dating back to 2006 won't be useful except for gaming games Offline.
Netflix does not offer any alternatives other than for users to purchase newer hardware. In particular, he states: "We hope you enjoy an even better Netflix experience on a supported device soon."