I personally believe sibling rivalry is a result of jealously and/or not feeling unconditionally loved.
Jealousy - Jealousy happens when one child appears to get an unfair amount of attention - they may be younger, be a high need child or are sick or disabled.
Unconditional Love - we all love our children and would do anything for them including giving our lives for them. Sadly our children don't always feel this.
Things that will help both situations.
Eye Contact - Use eye contact positively, look at your kids when they please you, when you hug them and say I love you. Don't stare kids down when they misbehave.
Physical Contact - Hug them, stroke them as you walk past, tickle them.
One on one time - if you have more than one child this is the hardest one to do but there are ways around it - each parent can have a date with each child each month (dates can be anything from going for a walk, a hot chocolate or a meal - a date is not sitting in front of a movie) , read to children individually, do a chore with one child (e.g. chat over the dishes).
As a single mum I didn't have the opportunity to have date nights, what I did was each night I sang to my children on there own (once they were 7/8 they asked me to stop since I can't sing) and I tried very hard each day to speak to each child individually, all my kids knew if they needed me they did need to let me know.