I think this depends on context.
If you are talking about a length of time, e.g. the playtime of a movie, I would use timespan.
When asking someone whether they have a moment to spare (because you need help or want to talk to them; I would use that phrasing: "Do you have a moment (to spare)?"
Each one has
His own piece of time
And his own piece of space,
His own fragment of life
And his own fragment of death.
That's a poem. Poems do not have to adhere to the same strict grammar rules. "Piece of time" is a bit weird in normal English; but you are justified in using it in your poem. Especially because it's made to mirror the other lines of the poem. "piece of" is repeated twice, and so is "fragment of". This is justification enough for you to use it.
So I think the best answer to your question is: poems do not have to follow grammar rules. Except maybe in cases where your poem would otherwise be impossible to understand (and when it is not your intention to be vague or confusing).