The most common and most likely answer to this crossword clue is the 8 letter word GOOGLIES
I've seen this crossword clue in Independent
G
O
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G
L
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More clues leading to the result GOOGLIES
Buddy explains!

The straight part
We know that "Deliveries" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case deliveries = googlies.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does GOOGLIES mean?
GOOGLIES noun- A ball, bowled by a leg-break bowler, that spins from off to leg (to a right-handed batsman), unlike a normal leg-break delivery.