Found some sources:
http://www.bbc.co.uk/dna/h2g2/A396029
“In 1485, following the deaths of his only legitimate son Edward and his wife Anne Neville, Richard sought to strengthen his hold on the throne and his political ties towards Portugal. Negotiations were under way for his marriage to Joanna, a sister of the King of Portugal, as well as one for his niece Elizabeth to marry his intended's cousin Manuel, Duke of Beja.”
http://www.r3.org/bosworth/texts/legends_princess.html
“Joanna's preference for the religious life, however, had earned her the title "The Holy Princess" in her own country, and she had already turned down offers of marriage with Maximillian, heir to the Holy Roman Empire (1472) and the young king of France, Charles VII (1485), for whom she was rather too old in any case, being one year older than Richard himself.
In August of 1485, the Ricardian negotiations came to a climax, according to Williams. The Portuguese Council of State urged Joanna's brother, King John, to accept Richard's offer. King John tried bullying; his aunt, Philippa, tried persuasion. The response, as Williams explains, was dramatic:
"Joanna retired for a night of prayer and meditation. She had either a vision or a dream of a 'beautiful young man' who told her that Richard had gone from among the living." The next morning she gave her brother a firm answer. If Richard were still alive, she would go to England to marry him. If he were indeed dead, [John] was not to press her again to marry."”
So unless you introduce deviations beyond Richard III winning at Bosworth, 1486 ought to see his marriage to Joanna of Portugal. Richard would be 33, Joanna 34. 1486 also ought to see the marriage of Elizabeth of York to the Duke of Beja, who later became Manuel I of Portugal. With these marriages tying England and Portugal more closely together, how might that have influenced events?
In OTL, Joanna of Portugal died in 1490, which would leave Richard a widower a second time at the age of 37, perhaps with one or two small children, who wouldn’t necessarily be male or survive to adulthood. (Half of Richard’s siblings had died young.) If nothing else, duty would require Richard to marry a third time and produce more possible heirs.