っこない is a combination of the 接尾語(せつびご) (suffix) っこ, and the い-Adjective ない. When attached to the 連用形(れんようけい) (masu-stem form) of verbs, it creates new い-Adjectives that express the impossibility of (A). (A) being whichever verb is used.
Common translations of っこない include ‘there is no chance of (A)’, or ‘doing (A) is impossible’.
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今年(ことし)中(じゅう)に30万円(まんえん)貯(た)めたいの?お前(まえ)の給料(きゅうりょう)じゃできっこないよ。
You want to save up 300 thousand yen this year? There is no chance you can with your salary.
どんなに鍛(きた)えてもあの人(ひと)だけには勝(か)てっこないよ。
No matter how much I train, there is no chance that I can beat him.
あんなデカい家(いえ)、どんなに貯金(ちょきん)しても買(か)えっこないよ。
I will not be able to buy a house that big, no matter how much I save.
Caution - Although extremely rare, as っこ stems from the kanji 子(こ), this grammar point may occasionally be seen in its kanji form.
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明日(あした)までに5ページのレポートとか、絶対(ぜったい)書(か)けっ子(こ)ないよ。
There is no way that I can write a 5 page essay by tomorrow.
こんな漢字(かんじ)だらけの新聞(しんぶん)なんて読(よ)めっ子(こ)ない。
There is no way I can read this newspaper that is filled with kanji.