By the time I was near the end of my stay in Ireland, I was sick and tired of eating potatoes.
この場合、次のような言い方ができますよ。
ーBy the time I was near the end of my stay in Ireland, I was sick and tired of eating potatoes.
「アイルランド滞在の最後の方には、ポテトを食べるのにうんざりしていた」
near the end of ... で「…の終わり間近」
to be sick and tired of ~ing で「〜するのにうんざりする」
ご参考まで!