"quick to forgive" is correct and usable in written English.
You can use it when you are referring to someone who is willing to forgive someone else quickly. Example: He was known in the community for always being quick to forgive, even after being wronged.
Crick was slow to anger and quick to forgive.
Unsurprisingly, Celtic fans were not quite so quick to forgive the treachery of their wayward Bhoy.
Do you believe that fans and the media were too quick to forgive and forget, charges dropped or not?
Sure, we rename our fried potatoes on a whim, but we are also relatively quick to forgive slights.
The punch is an accident, and he is quick to forgive John, whose mumbling, diffident demeanor is as disarming as his physique is imposing.
The public was quick to forgive, however, when Oh managed the Japanese team to victory in the inaugural World Baseball Classic in 2006.
Chalking it all up to "your father not being himself in those last few years," she was much quicker to forgive him than I was.
Always be ready to forgive.
Yet the positive polls following his speech showed how anxious Americans are for ennobling leadership – and how quick Americans will be to forgive other transgressions, if Trump acts statesmanlike.
I never actually encountered the type that was described to me as the ideal prosecution juror: the little old Lutheran lady in pearls — quick to judge and slow to forgive.
Those who prayed and studied with him in England, where he attended college from 2001 to 2004 and reportedly lived until weeks before the attack, spoke of a friendly associate who fervently sought an audience for increasingly extremist views but was quick to anger and slow to forgive.
