well it depends on what the irritating things are. I mean are they things she does, opinions she has, things she says, or what? I mean it's hard to train yourself not to be irritated by things like someone chewing with their mouth open or standing too close in your personal space, but if it's more part of who the person is, and how they behave, then I had this a while back with my MIL.
She gossips, she seems to enjoy falling out with other people/family members as she likes the drama, she defends FIL when he's completely wrong and it's hurting my DH, she spends money on ridiculous things, etc.
And all these things were irritating me, but I got over by realising that actually she was retired, very lonely, bored, feels like her purpose in life (the matriarch) has gone, and really that accounted for almost of of the above foibles. When I thought of it like that, I actually had some sympathy for her, she still does all these things, but I am more able to just humour her and think 'bless, she's just trying to fill up her days'.
I can even forgive her some of her non-PC opinions as the time and place in which she was brought up was never going to produce the most enlightened person, and that's not her fault, and it's hard to change these things later on in life.
But this wouldn't help if e.g. it's things like chewing with your mouth open!
D