Realise Your Mistakes
If you are sorry all the time, it does not mean you realise your mistakes all the time. Try to realise your mistakes and get rid of them if they are more frequent and common. This will help you to stop apologising all the time. Realising your mistakes also means you realise you do not need to be sorry all the time.
Honest to Yourself
Be honest all the time, especially if you have done something bad. Being honest and accepting responsibility of something done bad at your hands is also a way to convey your apology. If you are lying to yourself, then you will have to be sorry to cover up the matter. So always be honest and tell the truth.
Say Sorry When You Have To
You should not be saying sorry on every matter. For example, if you have done something in a wrong way, do it correct way on the spot so you do not need to be sorry. Just saying sorry does not resolve the matter itself, you should do something that compensates the loss of doing something wrong.
Say No Instead of Sorry
If you are not able to entertain a request of doing something for a person, do not apologise for it. Instead, refuse the matter straightaway, and be honest that you cannot do it. Here it is not your fault and you have not done something wrong for which you should apologise.