Death saves happen when you are unconscious. You cannot do anything, including delay, when you are unconscious.
If someone starts their turn in Spirit Guardians but wants to delay, they still have to make the save because they are there when their turn would have started. If that means you'd have to deal with the spell twice in a round - maybe consider not delaying (which there should be downside to doing in the midst of a frantic combat). Everything is supposedly happening nearly instantaneously anyway, so if timing is slightly off sometimes, I don't worry about it. But like I said if it became an issue we'd address it then. Pretty sure spirit guardians has not been cast in my games yet - but there are other spells that work similarly and it hasn't really come up much.