Yes Coturnix quail lay at night. According to some research I have looked at: "Most females lay eggs several hours before dusk"
(Konishi, 1980).
In the same article :ENVIRONMENT, WELL-BEING, AND BEHAVIOR, G. B. Chang ,*1,2 X. P. Liu ,1 H. Chang ,* G. H. Chen ,* W. M. Zhao ,* D. J. Ji ,* R. Chen ,* Y. R. Qin ,*
X. K. Shi ,* and G. S. Hu *
"Egg-Laying. Domestic quail and F1 often lay eggs
in the afternoon, mostly after 1530 h. No egg-laying
behaviors were observed in wild quail at daytime with
a harvest of 30 eggs, indicating that they lay eggs at
night."
2009 Poultry Science 88 :11371142
doi: 10.3382/ps.2008-00320
They are also referred to as nocturnal vs diurnal. More active in evening than day. Interesting birds to say the least. I love them.