We ought not to grieve or become irritated at anything because, by frequent vexation and irritability, we form the morally and physically very injurious habit of irritability, whilst by bearing opposition with equanimity we form the good and useful habit of enduring everything calmly and patiently.
The more wood you pile on a fire the more heat you get, and thus it is with God - the more you think on Him the more you are fired with love and fervor towards Him. He who loves the Lord is always mindful of Him, and remembrance of God begets prayer.
Not he is chaste in whom shameful thoughts stop in time of struggle, work and endeavor, but he who by the trueness of his heart makes chaste the vision of his mind not letting it stretch out towards unseemly thoughts.
If we prefer not to empty out all we possess for the love of God, let us at least not callously hold on to everything ourselves. Let us do something, then humble ourselves before God and obtain forgiveness from Him for what we have failed to do. For His love for mankind makes up for our omissions...
He who stands by a fire is warmed by it, and he who turns to the Lord with his mind and heart is warmed by the fervor of His love, and himself begins to return a warm disposition towards Him...The love of God is shed abroad in our hearts... (Rom. 5:5).
You ask for some way of completely eradicating irritability. The inclination to irritability is given us to use against sin, and we were never meant to use it against our fellow men. When we do, we act contrary to our true nature.