Both mean the same but the second sentence (아침에 일찍 일어나려고 어젯밤에 일찍 잤어요) is right. Both are understandable but if you want to be grammatically correct, the first sentence should be like this: 아침에 일찍 일어날 수 있도록 어젯밤에 일찍 잤어요. (일어나도록(x) > 일어날 수 있도록) But still, the second one sounds way more natural and most of people say that way.