The person in question here swims literally everyday.
"I think she really enjoys swimming (everyday? all the time?)"
It's hard to fit these use cases here.
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一日の楽しみ is not a common phrase, but I think it's almost the same as 毎日の楽しみ, or one's favorite activity which they do almost everyday. More typical examples of 一日の楽しみ would include 食後のビール, 昼寝, ネットサーフィン, 寝る前のゲーム, etc.
一日の楽しみ sounds like 'the fun part of a day' or 'the fun thing/activity that enables him to endure his daily work by being looking forward to that'. Good examples of 一日の楽しみs are already shown in Naruto-san's answer.
In Japanese, we often say "~を楽しみにして頑張る/耐える"-ish phrases, that is, "to work hard/to endure something by being looking forward to ~". 一日の楽しみ carries the nuance of such phrases.