Best case scenario for a surviving Vinland, is to have it discovered in the 900's, possibly have Erik the Red to bypass Greenland altogether, and first land on the sparsely populated island of Anticosti in the estuary of the St Lawrence River, or the island of Newfoundland. Trade with Iceland, such as selling timber and furs with the Icelanders in exchange for livestock, barly seeds, and iron ore (iron would be discovered in America at some point). Of course, the original Vinlanders should tell all about the rich lands and the comparatively warm climate of their new homeland.
About thirty or forty years after initial settlement, new waves of colonists could possibly be made up of disgruntled Norse Pagans, fleeing from places like Iceland and Norway, whom are fed up with the oppressive Christian regimes in their countries, or just aren't comfortable with the increased centralization of power in the nations of Scandinavia.
The steady exodus of Pagans that have braved the long journey across the Atlantic will maybe prompt further settlement on the mainland. Between fifty to a hundred years later, only ever smaller numbers of Norse people will be shipped to Vinland for a chance of a better life, if not to flee persecution.
Maybe some Irish or Germanic missionaries could arrive there, and whether or not they'll christianize as well is up to the author of the TL, but I would personally take the option of making the Vinlanders into the last nation on Earth that actively practices Norse Polytheism, which would make, among other things, some interesting dynamics when it comes to interactions with Native American cultures.
Limited contact with Europe may occur until the 1300's when possibly either Scandinavian or German Hanseatic League merchants sail to Vinland in their sturdy Caravels to make regular trading contact with them.
The Black Death being conveyed by European sailors, though, could be a potential disaster. But other than that, the construction of European style ships could encourage the Vinlanders to first sail down the coast, and make further contact with the Mesoamerican and Carribean cultures.
Within a hundred years of initial Norse settlement of Vinland, expeditions could be launched through the St Lawrence where the Vinlanders would discover the Great Lakes inland and the native cultures that reside there. Trade with the Vinlanders could could allow them to develop iron-working, ship-building, use of new crops, new animals, and animal husbandry. This introduction of new animals could potentially be the cause of epidemics, but despite the loss of lives, it may be a boon to their economy in the long run. The government of Vinland may start out like the Althing of Iceland, but may evolve with the cultural and demographic growth of the nation of Vinland.
They may be heavily involved with the native slavetrade during it's early history, although on the positive side of it for them, this may play it's part in boosting their population growth, even if it makes Vinland less ethnically homogeneous than when it started, but hopefully they'll be united in common culture, religious and political beliefs.
If Vinland is allowed to flourish, it will probably develop into one of the most advanced cultures in the Americas, while frequent contact with Europe in the early Second Millenium could allow them to challenge European Imperialism, whether Vinland is Christian, or it's original faith becomes codified and and developed enough to resist missionary efforts.