hi
amazing to think that you contact this forum and didn't know that there was a statue of him in tullow, another truly success story for this website!
Just looking at the census for 1911, there are absolutely no traynors in the county of carlow. Would his family had moved elsewhere shortly after his birth?
Also one thing worth considering, is that like other parts of co.carlow, the civil parishes are sometimes registered as a place outside the county, like where my relatives are in clonegal,to see their birth records you must look under shillelagh, in co.wicklow. I only say this as tullow is one of those towns that is not that far from another county border.
I also say this because, according to wikipedia, thomas was born 27 may 1881, that i would say that the civil birth that shane gave you was a year later?
I too have looked at the family search pilot and there is only one TT from carlow around that time, which is the 1882 one, though there is another that fits the age criteria and that is
william thomas traynor
april-june 1881
dublin south
volume 2 page 767
Hope this has helped
all the best
pete