Looks pretty cool. Like how you managed to generate the map.
For the rive you can choose an edge node and a node near the centre maybe,, or wherever really.
Use the Path function to get a list of nodes between the start and end node and walk that list to change the texture and perhaps a property of the node to indicate it is water. You might even choose a node near the middle, get its neighbours 2 or 3 tiles out and then generate and combine two paths to and from that "middle" node to make for a more bendy river.