日期 = "date", whereas 日子 = "day". Although in Chinese (as in English) they are sometimes interchangeable.
Ordinarily you'd expect a 日期 to have a numerical form:
What is the date today? Today is the 15-th April, 2020.
However, a 日子 isn't necessarily numerical:
What day is it today? Today is my birthday.
We typically think of changing the 日期 ("date") rather than the 日子 ("day").
Hello, I'm very sorry, I have to change my dates. Is that all right?
We also typically think of having a good 日子 ("day"), rather than a good 日期 ("date").
Today is a good day.