Remove the nest first and see what happens, also you could try and shorten the amount of light you give them. The one laying the eggs probably thinks it is the start of spring.

I have three canaries and I love them sooo sooo much. Firstly I bought two canaries Tweety yellow and Mango red. I bought them last summer in July 2013. Then I bought Tango white in April. Tango is not that cute because he is skinny and such a scaredy cat lol! Mango has laid 14 eggs in total they never hatched she ate all of them very long story no time to explain. She laid four brand new eggs and I think she has another egg because she's sitting on the nest now. Helpp because she is laying too many eggs. She is not stoping!!! I have heard that they came die if they lay too many eggs how can I stop her from laying eggs PLEEEEEASE HELP!!! I have also got a pic of her: Thanks very much