I may be wrong but I don't think any records were kept of passengers travelling within the British Isles. At the time it would have been all within the UK
http://www.liverpoolmuseums.org.uk/maritime/archive/faq.aspx
Ah, ofcourse - I was forgetting for a minute that Ireland used to be part of the UK.
Apologies for the delayed response, I've not had a chance to do any research for a few months - at present i'm looking to see if I can find a MI for Mary Ward m.d Stewart - I know she died in the Stirling Combination Poorhouse in Nov 1904, so would expect a burial nearby (however given it was the poorhouse she may have a paupers grave - therefore no stone!). I know nothing about James and can't find a definite link to him in a census.
Any help tracing Mary's burial might help, alternatively any help tracing Jame's death/burial would be helpful (He was still living in 1912 when his son Thomas married in Stirling and was recorded as deceased when Thomas died in 1959 in Scoonie, Fife).
Best Regards,
Martin