How about having girlJames married off to Edward Seymour, the other major claimant to the throne to sure up the succession? http://en.wikipedia.org/wiki/Edward_Seymour,_Lord_Beauchamp_of_Hache
It may be a wild card, but I think that is an interesting option: IOTL Elizabeth supported Henry of Navarre in his conflict against the Catholic League for the throne of France. So, what about the future Henry IV pushing further this alliance by offering his cousin Henry I of Condé as the husband of the young "Mary"? Between 1574 and 1586 he was a widower, and available to be married. Also, he was strongly Protestant, other point in favour of him. This way we would have a Protestant Bourbon England.
How about having girlJames married off to Edward Seymour, the other major claimant to the throne to sure up the succession? http://en.wikipedia.org/wiki/Edward_Seymour,_Lord_Beauchamp_of_Hache
Someone else whose marriage would have impact on young Mary (tho she might be also be named Margaret) would be her cousin Arbella Stuart since she is also in line for the English throne. OTL she ended up being imprisoned by her cousin James for marrying William Seymour (6th in line) without his consent. If Mary-Margaret also fails to have any male children but Arbella does then...