You'll find that there are two listings of christenings for an Elizabeth Cottier on the parish record page.

Here's the link to the Marown Parish christening page image, (close the gap be the two "t's.")
ht tps://familysearch.org/ark:/61903/3:1:9396-CYVL-N?i=40&cc=1784428

Here is the christening listing for the Elizabeth Cottier who I believe is the Elizabeth Corlett listed in the 1808 Marown, IOM will for William Cottier. (In looking at the page image, you'll see it mentions an illegitimate birth)
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Elizabeth Cottier

Isle of Man Parish Registers
Event Type Christening
Event Date 20 Sep 1778
Event Place Marown, Isle of Man
Gender Female
Father's Name Wm
Mother's Name Jane Quine
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If your direct line is Robert Corlett & Elizabeth Cottier, I'd appreciate any info that would let me know I have the wrong Corlett family.