You got to be able to stand firm with a solid no sometimes, even when they cry and throw a tantrum. They will learn next time to think before ask.
For their safety and health, we have to say no occasionally. For example, my daughter wants to eat ice cream for all her meals and wear summer dress all year long. Of course I won't let her. For the love of our children, give them what's good for them mentally and physically.
I have to train my daughter to understand not all her requests will be met. It's not kids' intention to be miserable but our responsibility to set boundaries. Actually they will feel safer and happier when there are clear rules and limits.
Children need you to verbally recognize their feelings sometimes. They cannot express it well yet. They cannot differenciate their emotions and feelings so they need your help. Lable their feelings at the moment of nagging and whining. Remember all kids want to look good in parents' eyes, no matter how bad they may behave. All the bad behavior comes from fear and anxiety of losing parents' love. They just want to test and prove you still love them.