Every dark cloud has a silver lining, but......

The Proverb Every cloud has a Silver lining conveys the message, one has to stay positive at all times and never lose hope at any cost. See a huge black cloud generally blocks the Sun fight and makes the atmosphere dull and dark . That is the Silver lining of a rough patch.

If we see successful people, very rarely we find an individual attaining success at the very first attempt. Because of their hard work and their firm determination to win, they became successful. Theory of Karma says, what ever you invest today, its returns will appear next day.

My opinion is, one should equanimus.  and also should treat both success and failure are the two faces of the same coin. Success is not a one day matter. With consistency and a strong Will to win, one can reach the pinnacles of glory.

I don't think Proverbs are contradictory to each other. They are the encapsulated knowledge of life. They often guide us.

I can find a connection between the two. The concept of karma is to make you streamlined and do what is good ethically and morally. Life is a journey and it will have bumps because it is a roller coaster ride. You will have dark clouds but you have to have a hope that there is a silver lining. There is nothing permanent and the good times will follow bad times and vice versa. The hope for that silver lining helps you build your trust and faith. With that trust and faith, you continue with your karma.

So with these two sayings, you stay hopeful and do not stray away from your good deeds even in the darkest of the times that life offers. 

Karma is nothing but action and every action gets a reaction , this is what Krishna says in Bhagavad-Gita. Unfortunately, some tend to connect it to destiny which is totally different since it goes much deeper than that. Change is a reality of life and no one is happy and unhappy all the time . If we are able to look beyond our grief of the moment,we will be able to see other positive outcomes ..