Looking on the internet deeply has found these results:

but not in day time is the most popular phrase on the web.

but not in day time but 10 results on the web	but not in day time 122 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
It doesn't look like this phrase is very popular! The search could not find any examples on the internet.	August 14 began to cough, feel feverish, and complain of soreness in chest. August 21 began to whoop and vomited four or five times a night but not in day time. Linking�... and early morning periods but not in day time periods. Effect of mango cultivars. The pattern (trend) of ant abundance is significantly different for cultivars (p�... Generally you are allowed to detect beaches, but not in day time during summer when people are on beaches and normally I would�... b ) In night time, we can find hiking boots ; but not in day time. So, when we switch day/night, we have a "time travel"... A real one!

but not in day time but

10 results on the web

but not in day time

122 results on the web

More popular!

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

August 14 began to cough, feel feverish, and complain of soreness in chest. August 21 began to whoop and vomited four or five times a night but not in day time.
Linking�...
and early morning periods but not in day time periods. Effect of mango cultivars. The pattern (trend) of ant abundance is significantly different for cultivars (p�...
Generally you are allowed to detect beaches, but not in day time during summer when people are on beaches and normally I would�...
b ) In night time, we can find hiking boots ; but not in day time. So, when we switch day/night, we have a "time travel"... A real one!