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.
The enemy of our salvation especially strives to draw our heart and mind away from God when we are about to serve Him, and endeavors to adulterously attach our heart to something irrelevant. Be always, every moment, with God, especially when you pray to Him. If you are inconstant, you will fall away from life, and will cast yourself into sorrow and straitness.
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.