What counts as an 'ancient'? Does Roman Empire counts? What exactly counts as 'daily'? Being daily written or intended to be read one per day? Or at some more or less regular intervals?

Anyway, Marcus Aurelius (while being Roman Emperor) wrote his aptly named Meditations in 161–180 AD. 12 books.

The book [i.e. "Meditations"] has been described as a prototype of reflective practice by Seamus Mac Suibhne - wiki

Lucius Annaeus Seneca wrote Epistulae morales ad Lucilium, a collection of 124 letters which weren't written 'daily', but at semi-regular intervals and many stoics were picking meditation themes from one letter a day[, week, month etc.].

Many ancient Chinese texts were also a source of everyday studies and meditations - I Ching, Laotse - Tao Te King for example.