After doing a little research, I have seen that there is some debate as to who is Miranda Keyes' mother. In Halo: the Fall of Reach, Dr. Halsey and Jacob Keyes start looking for SPARTAN-II candidates on August 17, 2517. In Dr. Halsey's journal, it states that Halsey and Keyes parted sometime around September 16, 2517. This is plenty of time to have an affair.
Dr. Halsey than had Miranda and eventually gave her to Jacob. In the September 1, 2525 entry in Halsey's journal, it says, "Did not expect the separation anxiety to be so strong. I guess not hearing her cry wakes me up at night too." Later, on July 12, 2531 she wrote "Jacob has agreed to take her in. I'll miss her, but it's for the best."
The April 6, 2550 entry is all about Miranda. It explains how Halsey has done everything in her power to dissuade Miranda to join the military. When she fails, she sees to it that Miranda is given one of the safest jobs in the military. Halsey says, "Initially, she likely joined the military to impress her father; after all, she had her name legally changed." From this, we can assume that Miranda Keyes was born Miranda Halsey. There are also drawings of what looks like Miranda as a child included in the entry.