There are many mature Chinese expressions that translates to "moment" as this word have many meanings in English.i.e.马上，一会儿，一下，就. And unlucky for you they are all common.
As a native speaker, I would recommend you to use the expression "a segment of time"(一段时间) to express the concept precisely at first. because when you say "a segment"(一段), it cannot be misunderstood.
Here's some detailed explanations.
瞬 have "eye"(目) on the left. think of it as a blink. the right side is its pronunciation, have nothing to do with meaning.
間 means a gap, a duration, a space.
so think of this word as your "in a blink of the eye"'s substitute.
刻 means to engrave (the right side is a blade, left is its sound). imagine you have a line that is time. you use a knife and point in the middle. that is a 时刻. it's not a period, but a point.
時候 is hard to explain as its a blurry concept, I'll just wait until someone modify my answer. but I would translate this word to "opportunity" or "when" rather than moment, i.e.
When will you come?
Come when you are free.
The time for harvest has come.