As the title says, I'm trying to write a character who's fairly positive in most situations and likes to be cheerful and upbeat, but this can quickly become irritating to some audiences, especially when they get in people's faces with their optimism and their idealism becomes unrealistic. Is there some sort of line I need to be mindful of when making concepts of her, such as how to not portray her as intrusive and single minded?
and their idealism becomes unrealistic.
I think this kind of answers your own question in a way. If your character is in a really hopeless situation that would be a good time to have them be maybe a little less optimistic. It's going to be more impactful if your character who's normally happy and positive just completely breaks down rather than acting like everything is sunshine and rainbows. It's more realistic too; we all get scared in certain situations.
Also, I would just make sure that you give her some other personality traits other than just being upbeat and positive (If you haven't already). No one likes a one sided character.
That's the thing, I don't know what else to put for her. I already have a tsundere (someone who's sweet but also has a temper) character and one that only gets mad when something specific is mentioned. I have a stoic, and emotionless doesn't suit her
If she's always cheerful this can often mean she's very naive, if you don't want to be that cliche when righting her story, give her a reason to be happy even when everything else is awful. I base many of my optimistic characters off of a person I know in real life who reacts well to bad things happening, His mentality is one that seems to solve many a problem. Things are already bad, being upset about it doesn't make it any better. Giving this to a character gives you an interesting opportunity to flesh out they're back story and when this Idea is explained at the right time, it can add a lot of depth to a story and help out some foreshadowing.
You could try going for an upbeat character who uses optimism as a sort of coping mechanism? That could give more depth to her beyond just being happy. Maybe she's been through a lot and being outwardly optimistic is the only way she knows how to deal with that? I guess that would make her kind of two faced though… Since you mentioned tsundere I assume you're pretty familiar with anime/Japanese content, so you could reference naturally upbeat characters from those shows to keep a clear reference. Gon from HxH, Honey from Ouran, Emma from The Promised Neverland, etc. etc. Those are upbeat characters that fans seem to love that have substance beyond their optimism.
Gon is a great example of a positive character that isn't annoying because of his flat character arc and the danger of being so stubborn, trusting, and unyieldingly optimistic. Have your character be so delighted with life and other people that she simply doesn't have time to be realistic, and then have a crushing moment in which something happens to completely shake her world view. In HxH, Gon is curious and trusting, so people who have trouble with emotion are drawn to him and become better for being around him. However, Gon's core belief (that the world is exciting and inherently safe) is shaken when his friend is killed, so he goes on a revenge mission, risking everything. He cries. He's broken. And the effect of his departure from his usual sunshiny self is felt by every character. There are many directions to take an upbeat character (Aang from Avatar, Leslie Knope from parks and rec, spongebob, ant man) so have fun and don't worry about being annoying!
Angst. Break them. Make them depressed under that happy facade. Or, make them optimistic but grounded. Hoping for the best but aware bad stuff happens, and willing to offer support for that. Or both. Idk I'm not good at explaining stuff.
To add depth and make an upbeat character less annoying, I recommend that you put a story behind the smile. Maybe they’re hiding sadness and insecurities behind their go lucky personality. That’s just one example, as long as you add multiple personality traits and avoid a flat character.
I have a character named Blue who is very bubbly and optimistic, but she's not annoying about it at all. But, to get a more realistic feel, break them. Make something happen that affects them negatively, and make them have a realistic reaction.