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 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.