Hi Penny
The Old Parish Register entries pre 1855 are sometimes patchy. You may be able to find other siblings' births and christening details but sometimes not the one you are looking for which is a pity, but not uncommon.
One way for you to double check on William's parents' details would be on his second marriage entry to Margaret Risk on 15 JUN 1858 Tradeston, Glasgow. Given that this is information he himself would have given, it is always worthwhile checking this source also.
Mother Margaret Crawford shows on family trees witht the following details: Born on 23 June 1766 and died on 12 Apr 1856 in Paisley Road, Glasgow. Buried in the Churchyard at Irvine. Sometimes also worth checking death certs of parents to see whether the name you are researching shows as an informant/witness.
Penny, not sure how much information you have on William and family already. I am assuming you have his census details to his death in 1880?
His Will entry shows on SP on 20/01/1881.
Monica