Supposedly, Tom Marvolo Riddle cannot love because he was conceived with the help of a love potion. That is what sets him on the path towards becoming Lord Voldemort. Change the rules of the universe so love potions don't do that, and you're fine. 

However, if you are also making other major changes (such as Hermione having an incident with her time turner and winding up at Hogwarts together with Tom) please take the time to make the counteraction of the love potion a minor change instead of a major one. It is certainly possible to do that with the premise we are given when Lily sacrifices herself for Harry. Merope, Tom's mother, died giving birth to him. Suppose that she loved her son a lot, and, even knowing that she would not be able to take care of him, wanted to ensure that he was cared for; beyond just the Blood Purist ideals of continuing the line that would have been drilled into her from birth (or perhaps in spite of, since with Tom Riddle Senior being a muggle, she was certainly not continuing a Pureblood line). That could have been enough to provide the same protective energy as Lily gave to Harry, and Tom's protection could take the form of allowing him to have some slight capacity for love, instead of how Harry was protected from the Dark Lord. 

The way I imagine it, Tom would still grow up essentially unable to love, and this would be only encouraged by conditions in the orphanage. He would be the same when starting Hogwarts as in the original books, but eventually (sometime before Tom became embroiled in the Dark Arts enough to even consider making a Horcrux, but probably not before he had taught himself at least a few dark spells) some other person would become attached to him, and them truly caring about him would combine with the lingering protection from his mother to allow him to care back. This person would not necessarily have to be a girlfriend (or boyfriend), and in fact perhaps it would make the most sense for it to be some sort of parental figure, to make their love for Tom attach to Merope's lingering love more smoothly. Either way, it would make it possible for Tom to slowly start caring about people, and each new friend or crush would help push back the effects of the love potion a little bit more until they were all gone, except as memories.