Reach out on family functions:
Whether it is a dinner, funeral or a family get together, try to be in the same group as the sibling and blend in casually. Ask about his/her job and family and discuss about people or objects that you both are mutually concerned about like your parents health.
Write a letter:
Write an emotional letter placing an emphasis on how important is family in one's life and how much you miss the other person. It could have references to your past happy times together, may be as kids. You could also include pictures of yourself or your kids to serve as an emotional flash back.
Give a phone call:
It is the best way to break the ice because it is so direct and has the advantage of hearing each other's voice which is enough for healing some broken relationships. Give a phone call and be casual about it. Do not give or demand any explanations for thee past issues but make sure that you communicate it well that you want to continue being in contact and mending it.
Send greeting cards:
If you do not want to be as emotional or direct as sending a letter or a phone call, send a greeting card instead. It is a subtle way of letting the other person know that you still think of them and have not given up. Send the cards on birthdays and other important occasions to pass the message that you remember.