"Coaches' gifts" is correct, but I prefer the phrasing suggested by Thumper in #13.
Regarding the invitation, it would be better to lay out the names of the students in two short columns or something of that sort, and forget about commas and other punctuation. IMHO, the text of an invitation should be laid out attractively using centering and line breaks and the like, not treated as if it were a regular sentence.
[Once an editor....
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