〜きり details

きり

just that many and no more — 一度[いちど]きり, 二人[ふたり]きり

あの人ひとと会あったのは、一度いちどきりだ。

ano hito to atta no wa, ichido kiri da.

I met him exactly the once, and that was that. neutral

今日きょうは二人ふたりっきりで話はなしたいんだけど。

kyou wa futarikkiri de hanashitai n da kedo.

I'd like to talk today with just the two of us. casual

Examples

just that many and no more — caps a count, usually a small one the speaker presents as meagre

あの人ひとと会あったのは、一度いちどきりだ。

ano hito to atta no wa, ichido kiri da.

I met him exactly the once, and that was that. neutral

残のこっていたチケットは、二枚にまいきりだった。

nokotte ita chiketto wa, nimai kiri datta.

There were only two tickets left. neutral

一度いちどきりの機会きかいですので、ぜひご参加さんかください。

ichido kiri no kikai desu node, zehi go sanka kudasai.

This is a one-time opportunity, so do please join us. formal

just the two of us — on a count of people, きり adds that nobody else is there

今日きょうは二人ふたりっきりで話はなしたいんだけど。

kyou wa futarikkiri de hanashitai n da kedo.

I'd like to talk today with just the two of us. casual

子供こどもが独立どくりつして、今いまは夫婦ふうふ二人ふたりきりで暮くらしている。

kodomo ga dokuritsu shite, ima wa fuufu futari kiri de kurashite iru.

The children have moved out, and these days it is just the two of us at home. neutral

っきり — a small っ added for emphasis, spoken only — 一度いちどっきり, 二人ふたりっきり. It grumbles or it gets cosy, where plain きり merely counts.
きりで — で hands the capped count on to a verb — 二人ふたりきりで話はなしたい。
きりになる — the count becoming that small is the event itself — 子供こどもが独立どくりつして、夫婦ふうふ二人ふたりきりになった。

Not the きり of つきっきり, which hangs off a verb and means never leaving
something's side.

だけ
だけ is the neutral "only" and takes any noun at all, and verbs besides (水みずだけ, 見みるだけ); きり needs a counted amount and adds a verdict on it — 二人ふたりだけ merely counts two people, 二人ふたりきり says there is nobody else there.
しか〜ない
しか demands a negative predicate somewhere after it and points at the shortfall (千円せんえんしかない); きり needs no negative at all, which is why 一度いちどきりのチャンス is an ordinary noun phrase and ×一度いちどしかのチャンス is not.

たきり
The same limiting きり on two different hosts — after a た-form verb it says nothing has followed since (家いえを出でたきり帰かえらない), after a count it simply caps the count (一度いちどきり); only what sits in front of きり tells the two apart.