A/N- Different to the original ending planned, but I had this story and nowhere else to fit it, and realized it fit better here.
Here is what happened on the other side of the TARDIS...
They had just gotten the earth back into its rightful spot in the sky, when there was a loud knock on the TARDIS door. They heard a distressed woman's voice on the other side of the door.
"Doctor! It's time! Open up and help me!"
Confused, the Doctor was about to run down when Jack went forward instead and opened the door.
"Jack Harkness! This certainly is a surprise. Is my old man in there?"
"Wha-"
"Well, let's just have a look, shall we- ahh!"
"Jack, who- River Song?"
"Hello Sweetie- oh, daft old idiot- how young are you?"
"I'm not- hang on," he said, finally registering her look of pain and her hand placed delicately over her-
"River… is- I mean. Are you pregnant?"
"Not for much longer- get over here!"
The stunned Doctor and his clone ran to her when she screamed once more. Jack held her up as pain contorted her face.
"Hands above the equator at all times Captain," she said when the contraction had passed. Then she took in the other men near her. "Two of you! Well, is it my birthday as well?"
"Doctor- who is this?" asked a very confused Rose, while Martha went into medical mode and ran to her newest patient, taking vital signs and checking her pulse.
"River, why come here? To me?"
"It's not like I had much choice, Sweetie, kind of got distracted. I was on the moon helping with a last- minute treaty, then the earth moved and with its gravitational centre gone, everything went haywire up there. It returned to normal not long ago, so of course I knew I'd find you close by. By then the contractions had started."
"But Doctor, she can't be-"
"Donna! Spoilers."
"Doctor, not to rush you, but this whole room will be getting a very big spoiler very soon if we don't move her out of here- this instant," Jack remembered his daughter's birth and was not sure everyone here was ready for such an up close and personal experience.
"Right- River, med bay- now."
River got a death grip on the Doctor's hand as Jack helped lead both of them to the med bay, Martha listing out instructions for what sort of supplies she would need, with which Jack hurried to comply.
As Martha continued shouting out orders for the two flustered men, River's grip tightened on the Doctor's hand- which she periodically squeezed every time her body demanded its visitor leave.
After that was a whirlwind of activity as Jack played nurse to Martha, who confidently doled out instructions whilst River grabbed the Doctor's hand, clinging to him for steadiness every time another contraction wracked her body. She grimaced and breathed, trying to catch her breath and concentrate on having her baby. She should have known that man wouldn't make it so simple.
"Again, mind telling me why you're here, Miss Song? With me?"
"Because… you're my best friend. Or worst enemy. Hard to tell sometimes. But you like that sort of thing, don't you?" she teased, gasping and groaning through another contraction.
"You know," interrupted Jack, "we have tablets on board from New Earth. No pain, no problem. Just pop it in and rest until it's time to push."
River glared, sweat pouring down her face as her baby grew more and more anxious to meet her.
"We don't know each other yet, Jack. But suffice it to say… I know pain. I know agony and sorrow and yearning and tears. And all of that has been against my will for the sick pleasure of others and in the service of hurting people. And if you think for one second that I'm going to pass up the one opportunity I'll have to feel pain on my terms, and in the service of giving my baby life, well, let's just say we won't be acquainted for very long."
At that Jack put the tablets back in a drawer, taking up position on the opposite side of River from the Doctor, holding her hand through another contraction.
The Doctor stayed by her side as Martha called Jack off again, breathing with her and watching the machines hooked up to her, interpreting the TARDIS' data. He kept telling her stories, anecdotes, and things he had "fixed" throughout history, and she rolled her eyes at him, telling her own version of events as told by her research, fondly calling him an idiot, and gasping as pain seized her, this time stronger and longer than the others.
"Best friends, huh?" he tried distracting her again.
"Something like that," she said, sitting up and closing her eyes again.
"Or worst enemies," he muttered to himself. "You don't feel like the Master."
"Spoilers," she said with a small smirk before breathing deeply once more.
"Well, good. Good to know. So this baby-" he began.
"What about my baby?" she raised an eyebrow at him.
"Well, I mean… will I… be involved at all. In his or her life?"
"You seem pretty involved right now, Sweetie."
"Yeah well… I mean… children are-"
"You're saying no matter who I am, you want to play with the cute baby?"
"… little bit?"
She huffed out a laugh, regretting it instantly. "Sure Sweetie. Dote on my child all day lo-oooong" she cried, looking to Martha, who checked her progress.
"Looks like you're almost ready to push, River," Martha said.
"I'm not," she whined, taking a deep breath and trying to concentrate. "I- I need a moment. Just a moment by myself to prepare. Please."
Martha looked at her face, then at her progress, then gave a quick nod to the two men. "Two minutes, we can get some things for when the baby arrives."
Martha, Jack, and the Doctor walked out, and she asked the TARDIS to dial a familiar number.
"Hello?" Amy's voice answered, before an image of her appeared next to River's bed.
"Mum! I'm in labour, onboard the TARDIS. The Doctor's here, but not my Doctor and I don't- I don't think I can do this."
"Of course you can," Amy encouraged, "Gotta meet your daughter, after all. Rory! River's having the baby!" Rory came into view as well. River shook her head, moisture in her eyes.
Amy's hologram reached out and grabbed River's hand. Rory kept his eyes on her face as she concentrated.
"I can't, Mum, I just can't. He doesn't even know!"
"You can, River. Melody Pond can do anything."
"River," Rory bent to whisper in her ear, "he will know. And he is here. And more importantly," he smiled, "you're about to meet a very important little girl who adores her mummy more than life itself. You just have to get through this one difficult part, first."
She looked at them, scared but comforted, then screamed out for the Doctor as the baby refused to stay put a moment longer.
"River," breathed the Doctor, immediately running over to her and looking down at Jack and Martha as they prepared for the delivery, "you're amazing. One of the bravest, strongest people I've ever met. This child is lucky to have you for a mother. Now, we need you to prove what a wonderful mother you can be- and PUSH!"
She bore down- Jack, the Doctor, and Martha all encouraging her as she kept in mind the reason she was doing this, testing every limit she had previously thought she had.
"One more push, River- you can do it!" encouraged Martha.
With a final grunt and a shout to the ceiling, a new Time Lady made her way into the universe.
And when all was said and done, and all the tests had been run, Martha laid the baby in the Doctor's arms to pass along to River. As he stared into deep green eyes and felt a tiny hand clasp tightly around his finger, he was rendered nearly speechless by amazement, only two words making it past his lips.
"Mia Bella."