"오빠 오늘은 제 생일인데요. 생일선물로 하트를 보내주면 안되나요?" That sentence looks fine. You could also use a different ending, like "하트를 보내주실래요?", "보내주실 수 있죠?", or "보내 주시길 부탹해요.". 안되나요? sounds a tiny bit serious to me, but it might just be my own sensitivity. EDIT: As Banaan mentioned, 보내주면 안 돼요? is also good (I think better than 안 되나요?). Also, most people would say 오늘 제 생일인데요 without 은, although it's not wrong to include it.

This is so cute hahahha~ I could also recommend just making the ending 안되요.