Hall, 27, has previously featured for Bradford Park Avenue, Brighouse Town, Silsden and Thackley before joining the club from Farsley Celtic.
Kenyon, 18, joined the club in the summer of 2020 following his release from Sheffield Wednesday.
The club has also confirmed that full-back Clark Greaves and Harrison Foulstone have departed to play football in the USA.
Stocksbridge Park Steels added: "Harrison will be playing in Pennsylvania for Shippensburg University. The club would like to place on record our appreciation to both players during what was a tough period for everyone during the pandemic and wish both players good luck in their futures in the USA."
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