I would say that the key would be the Dutch keeping New Amsterdam/New Netherlands during the Second Anglo-Dutch war somehow. Since during the third Anglo-Dutch war, the Dutch were strong enough to even recapture New Amsterdam and not long after the glorious revolution happened and the Dutch and English were allies for a almost a century. Time enough to keep the Dutch identity of the region and significantly change North American history.
So if the key is the second Anglo-Dutch war, the Dutch must either be willing to trade Surinam back for the New Netherlands, which is hard, since Surinam is worth a lot more than New Netherlands , or the Dutch capture some British area that is worth less than Surinam, but would be a good trade for New Netherlands (maybe a southern North American British colony) or the could capture both Surinam and that colony or they could never lose the New Netherlands colony. I think the easiest way is letting the Dutch capture some colony instead of Surinam.
So my proposal would be that the Dutch lose the New Netherlands during the Second Anglo-Dutch war, but manage to capture Carolina (unless someone can think of a better colony?), instead of Surinam. After the war the New Netherlands is traded back for Carolina. Surinam remains English and the Dutch expand in Guyana (so we are switch the Dutch and English colonies here). To protect New Amsterdam better the area is fortified and the WIC (Dutch West Indies Company) loses control over the New Netherlands (New Amsterdam was already lost to them, the Dutch Estate General ruled it). The Dutch manage to defeat English attacks during the third Anglo-Dutch war and after the glorious revoltion the English and Dutch are more friendly. They help each other with the wars against France, although, because the Dutch actualy split the Neglish colonies, they aren't able to defeat the French.So the French manage to keep (some parts of) New France. The New Netherlands is unable to expand into the backlands, as the English colonies do, partly because it is smaller population wise than the English colonies, so it remains roughly the area of New York/New Jersey. In the 18th century it becomes effectively a Dutch Dominion. It has a lot of autonomy, like the Dutch provences, although no representationin the Estate General.Basicly it has the same situation as Drenthe had (not quite a provence, but better of than a generality land, certainly better of than a colony). Interestingly this leads to the Cape colony demanding the same rights as the New Netherlands has. Since they were ruled by the far more succesful VOC (Dutch East Indies Company), that is quite a bit harder, but when the VOC is in hard times, they get it too. In the 20th century, maybe even the 19th century the New Netherlands becomes effectively an independent nation.