If you are saying that you are asking for time to complete some task or to prepare for something, the normal way to phrase it would be, "Please give me one day."
It would be grammatically and technically accurate to say, "Please give me one day of time". But no one says that, because a day is a unit of time, and so to say "one day of time" is redundant. As opposed to what, a day of height? Well, I suppose you could imagine some context where it might be unclear without specifying "of time", like if you had just been talking about "a day of sales" meaning the amount of money the company made in one day, or something of that sort.
"One day at time" doesn't make sense. People do say, "one day at a time", as in, "I am going to deal with my problems one day at a time", meaning, I am not going to worry about the long term, but just worry about each day's problems as they come.
"One day time" doesn't make sense here. We do say "day time" to mean the part of the day that is light, as opposed to "night time". But I don't recall ever hearing it used with a number. You might say, "I like to walk in the park during the day time", meaning you want to do it when the sun is up rather than when it's dark. But people don't say, "I spent three day times working on this." I've just never heard the phrase used that way.