I haven't even been able to find a proper date for the Renwick Cockatrice or more correctly crack-a-christ). Some source say 1733, others 1620. Given the vast number of basilisk cases all over Europe in the first half of the XVII century (Rome, Prague, Vienna etc) I favor the earlier date.
A very interesting part of the story is the fact that the Tallantire family was given exemption from tithes following this feat. If I remember correctly since 1530, after the Abolition of Monasteries, tithes had to be paid directly to the Crown. If the Tallantires obtained their exemption after this date there should be some trace of the feat. Unless, of course, it went conveniently lost during the Civil War...
A popular line, though, gives the date as "during James I reign" (1603-1625), which will of course confirm the earlier date.
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Fas: Ite, Maledicti, In Ignem Aeternum.