None of their children believed their mother was capable to kill herself.

英訳に間違いが有れば正してください。

子供たちの誰も彼らの母親が自殺する可能性を信じていなかった。
None of their children believed their mother was capable to kill herself.

ヒント
形容詞の用法

答え to killをof killingにする

None of their children believed their mother was capable of killing herself.

be capable of doing
doingが可能である