Learn English – use ‘yesteryears’ and ‘yesterdays’ if I want to refer to ‘dayS’ and ‘yearS’ in that period

I'll be referring to the definitions of count from Oxford Learner's in my answer.

Don't count is the closest to an opposite for count in the sense of numbering in sequence (definition 1). There's no pure antonym here; what could be the opposite of saying "1, 2, 3..."? Some thesauruses list words like guess as antonyms for this case, but I strongly disagree with that.

Definition 2 means calculating a total by summing up the number of members. This is the sense used in your example (let's count... ten in total). As with definition 1, there's no true antonym, for the same reasons. Similarly, you can get the right essential meaning with don't count, and it would be correct to use in your example:

And thus, if you don't count me, you are nine.

But we can get better results with definition 3, include. Exclude is its appropriate antonym. It's also correct to say it in place of discount in your example:

And thus, if you exclude me, you are nine.

Using exclude causes a definitional shift in the usage of count (changing from 2 to 3), which technically changes the meaning. Outside of situations where semantic pedantry is part and parcel (e.g. the law, professional philosophy, ridiculously close linguistic analysis, internet arguments), nobody will care about this. Everyone (discounting those who don't know enough English) will grasp the meaning without any problems.

Since you've discounted don't count, exclude is the best choice.

Definitions 4, 5 and 6 all have the same antonym: discount. See definition 1 from OALD, which I actually find rather lacking; discount can also mean ignore, not include, minimize, etc. MW is more complete here.

Discount is in your example. While semantically (and grammatically) correct, discount is too formal for the context, making the response sound strange. For a group of people organizing a trip together the phrasing just sounds weird, though the meaning is clear. Using discount makes count definitionally shift, as exclude does. However, here the "distance" between the definitions is noticeably greater and makes the change awkward; in general conversation, people will stumble over this. Exclude is a better choice.

OALD redirects uncount to the entry of uncountable noun!

That's because it's a standard abbreviation for uncountable [noun] in dictionaries. But as you've found out, it's not a word in and of itself.

You've clarified that you're after le mot juste to complement count. I agree that count/exclude and count/don't count aren't as eloquent as a cognate pair, such as include/exclude. However, I'm afraid my vocabulary's at an end here; I don't know of a single-word, etymologically related antonym for this sense of count.

For a simple drop-in replacement, I recommend exclude or don't count. I realize that's not what you're after, but in terms of an easy, quick and accurate solution this is the best way to go. Additional apropos alternatives:

• Use include / exclude instead of count / antonym-of-count.
• Restructure the passage to use with / without me or something along those lines, as suggested by Damkerng T.

If your heart is dead set on some sort of count pairing, you could use discount, but I think it's self defeating to use an awkward, contrived sounding phrasing for the sake of preserving a nice juxtaposition of vocabulary. If you're going to do so, I suggest using counting/discounting and upping the formality for the sake of making things marginally less peculiar. Something along these lines, for example:

OK, we are ten, counting everyone, but mind that I might have some unavoidable work that day. Discounting me and planning for a group of nine might be wise. Please arrange for the food and accommodation accordingly.

Bear in mind that while these sentences are now consistent and don't mix registers, they are still too formal for the context. Someone planning a vacation with friends and who's been using phrases like you guys should expect to receive some quizzical looks if they start talking in this fashion.

Come and sit. I want to tell you the story of my life.

Though the story of my life is often used to describe something bad that happened multiple times in your life, e.g.

I asked the new girl at work to go out for a meal - and she got off with the waiter. That's the story of my life!

(source: Wiktionary)

it can also be used in the context you describe, cf. this article:

But it's not stupid at all. Though perhaps the facts of someone’s life, presented end to end, wouldn't much resemble a narrative to the outside observer, the way people choose to tell the stories of their lives, to others and—crucially—to themselves, almost always does have a narrative arc.

The story you want to tell will no doubt have 'something bad' that happened multiple times (probably many of them) so I feel using this particular idiom is warranted here.

Alternatively, you can use the phrase you already mentioned, life story:

Come and sit. I want to tell you my life story.

The Free Dictionary defines it as:

an account of the series of events making up a person's life

but this does not carry a negative meaning per sé.