He would have remained single. That is what is most probable. His upendo for Ginny was true and deep. They were both passionate for each other's love. Unlike other infatuations(like the one Harry had on Cho),he felt for Ginny like he truly wanted her and had already decided on her as a life-partner(if he would have one).
We saw the depth of his feelings when he could not kubeba Ginny's words of praisings at Dumbledore's funeral.He could not look her in the eye when he told her that they had to end their relation.Yet,he never stopped loving her as we saw in the 7th book. As he started the winded journey with Ron and Hermione,he thought of Ginny and worried for her.Remember when Ron left him(probably the darkest saa of his life),he stared at Ginny's dot in the marauder's map,all the time praying for her safety. And it was for the sake of her happiness and safety in the first place that he broke up with her.
He loved her as well as anyone could and it was probably one of the most blissful moments of his life,getting married to Ginny. If Ginny had died in the battle(although I don't even like to THINK such),Harry would certainly NOT marry anyone else.It would have seriously undermined the whole Harry-Ginny relationship.
I think he'd mourn Ginny for a long while, then maybe eventually marry a new, unknown character. He wouldn't marry Hermione because that'd mean stealing his best friend's girlfriend au wife. I don't think he'd marry Luna because she was such Marafiki with Ginny, he'd keep being reminded then.
For the most part I believe he would have stayed single. IF he married anyone else it would be Luna. Ron and Hermione Loved eachother deeply- Harry knew that, he would not marry Hermione and they DO NOT and WILL NEVER belong together, same with Draco and Hermione. Rowling spoke out of context which she admitted herself after she AGAIN impulsively spoke about Ron and Hermione. And I say again for the millionth time - they would not need marriage counseling anymore than any other couple in the world. No couple is perfect. I upendo JO but she says things she shouldn't sometimes.