as you have prob found by now very few registered births pre 1850 (less than 60) and none that meet your couple.
Lindsay is generally a scots name (there was just one in IoM in 1841 tho there was an Irish Roman cath Lindsey family).
The usual Manx name (long established) was Woods rather than Wood but no match I can see in 1851.
If transient visitors then may well have registered the birth elsewhere (or baptised elsewhere esp if Scots Presbyterian) - not sure when Scots civil reg came in but think post your date.