Boil the sweet potatoes in large pot of boiling, lightly salted water until halfway cooked, about 5 minutes. Drain and cool. (Can be prepared one day ahead. Cover and refrigerate.)
Combine cider, sugar, butter, salt and allspice in heavy large skillet over medium-high heat. Bring to boil, stirring often. Add sweet potatoes and cook 5 minutes. Add dried cranberries and continue cooking until liquid is reduced to syrupy glaze and sweet potatoes are tender, about 10 minutes.
Season with salt and pepper. Transfer to bowl. Sprinkle with green onions.