Cook sweet potatoes in large pot of boiling salted water until halfway cooked (a knife inserted into center will encounter considerable resistance), about 5 minutes. Drain and cool. (Can be prepared 1 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 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.