Sincerity is the gist of pure intentions. But, no sincerity has been proven yet, without actions.
It is indeed difficult to convince one person to believe in you. No matter how tight your relationship with the other individual, trust is always an issue. Sincerity is always questioned.
How do you deal with it?
Is there anything else you can do?
Of course, there is always a way to everything.
First, be true to your words. Earning trust is about respecting your words and respecting people around you. Do not make promises that are beyond impossible to happen. Speak less, but do more.
Second, exert some effort. A continuation to the first one in proving to another person that you are sincere about what you said is to give him or her things beyond expectations. If you wish to gain something, and this time, it is trust, then make some sacrifices.
Most of the time, you only have one chance to prove how sincere you are. Make that moment special. Do something. Give respect and earn trust.
Once you are able to deliver your actions sincerely, then that could open an opportunity. For relationships, it could be the start of a good love story.