Hi,
Sorry no, I don't have a DOB for James but the census suggests 1835/1836.
From the school Michael is attending in 1881 the family could be Roman Catholic. I have no experience of finding RC records, but I'm sure someone else here will be able to point you in the right direction

I think this might be James and Mary in 1861, same address but HOLLAND looks like HOLLORAN

1861 RG09/3377 f.62 p.20 Leeds
55 Wellington Yard
Michael HOLLORAN Head M 47 Brush Hawker Ireland
Bridget " Wife M 47 Hawkers Wife "
Mary SHERAN Daur M 22 Work at Flax Mill "
James " Son In Law M 23 Bleacher "
Michael HOLLORAN Son Un 13 Cloth Dresser Leeds Yorkshire
Martin " Son 9 Scholar " "
MarriageJames SHEARAN Dec Q 1859 Leeds 9b 625
Mary HOLLORAN
This marriage cert. should give you James father's name.
Do you have Michael's marriage cert. to check who his father is?
Regards,
Daisy
Thanks Madri for showing the other post, I'd already typed all this out so I'll post it anyway. Maybe a Mod could combine the threads.