The only births showing in Scotland, to parents named Andrew Wylie or Wyllie, and agnes Pollock, in that timeframe are as follows
Alexander Wylie, born 8/Oct/1826. Stewarton, Ayrshire,
Agnes Wylie, born 30/June/1829. Neilston, Renfrewshire,
Janet Wyllie, born 26/June/1831. Kilmarnock, Ayrshire,
Mary Wyllie, born 27/Oct/1837. Kilmarnock, Ayrshire.
Not all births in Scotland, prior to 1855. were registered or were indeed required to be registered, many births that were registered did not survive the course of time.
The three places you mention in your post ie Neilston, Dunlop, and Stewarton, are close to each other,
The marriage of Andrew Wylie, and Agnes Pollock, was noted in both Dunlop, and Stewarton, on the same date 21/Feb/1826. meaning that Andrew, and Agnes, were resident in those places at that time not neccesary born there, ie Andrew, perhaps Dunlop, and Agnes, perhaps Stewarton.
If you look at the order of the four births above ie first born etc, then those first three would fit the Scottish naming system for the period, ie Alexander, first born named after Andrew's, father from Neilston, second born Agnes, named after Agnes's, mother Agnes Gilmour, and third born Janet, named after Andrew's, mother Janet Clark.
Another possible clue Agnes Wylie, born 1829, was born in Neilston, just possible Andrew, and Agnes Pollock, were visiting Andrew's, parents at the time of birth.
There may also be other births to Andrew, and Agnes, that did not survive the test of time.
The above family do not appear on the 1841 census for Scotland, so a likely departure date would be sometime between 1837, and early 1841.
Regards,
Jonn.
