It's one thing to have a deliberately annoying character, and another for a character you love to seem annoying to readers. You can't entirely control how other people will feel about your characters. Nor can you please everyone.
That said, there are a few things you can do to help your characters' odds. This list takes you through them.
Make Them Sympathetic in Some Way
A character who always follows the protagonist around craving attention and validation might be annoying unless we know why they’re doing that.
Maybe they feel abandoned by everyone and they’re over-compensating. Maybe they’ve been ostracised so long that they latch onto whatever scraps of attention they can get.
A “tragic” backstory doesn’t magically make an annoying character less annoying, but giving their annoyingness some context can help. to humanise them.
Don’t Reduce Them to Their Quirks
If a character amounts to something like “the fashion-obsessed one” or “the avocado hater” (me) then chances are they could use some depth (unless they play a very very minor role).
We should be able to understand more about the character than just their main quirks. If you need a hand fleshing out your characters and making them feel like real people, check out the character workbook.
Avoid Constant Negativity (Unless That’s the Point)
Unless you’re deliberately writing a whiny character, balance the whining with proactivity and positive moments if you want to avoid your character becoming grating. It’s normal for characters to have low moments.
They might vent to their friends or feel hopeless and start to despair. Normal! But consider balancing these moments with moments of hope or enjoyment, or it could get a bit tough to read. Depends what kind of story you’re trying to tell!
“Show Don’t Tell” the Things They’re Whining About
Yes, another slide about whiners, but I’ve noticed a lot of readers have an extremely low tolerance for very whiny characters. If your character is always whining about how her friend is unreliable, show us how that impacts her. Show us how she misses an important appointment because she was stood up by her friend. Show us what that means for her life.
Allow Them to Change
Making your character start off as annoying is a great way to set them up for a dynamic character arc. Maybe they start off as a whiny, spoiled noble, then they eat a bunch of shit, learn, and grow.
Mine it For Comedy
Annoying characters can be pretty funny. Generally you might want to avoid giving them too much “screen time” (page space?) though, but it’s your call! See what your beta readers say.