the 'reference' book you mention is IMO in many places poorly researched (eg have a look at www.manxnotebook.com/iomnhas/v054p411.htm from where she took often the exact words) though I'm not sure I can supply the answer.
There are two pubs opposite each other in the forecourt leading to the Station at Castletown (which is situated on the outer edge of the town).
One was built shortly (c.1876) after the railway opened - 1873 - this was known for many years as the Duck's nest supposedly as its owner was a Mr Duck and may well be your station hotel (now renamed The Sidings) though originally it was a woodern building and in 1881 census I can't locate any occupant. George Duck was postmaster at Castletown for many years but died 1861 so any Mr Duck must have been his son though again none are found in 1881 census; the adjacent inner harbour is however also known as the duckpond. The other was the more impressive Castletown Hotel but later renamed the Viking built around 1900.

There was a Station Hotel in Castletown c.1905 as Richard Cain (shortly to be involved with Castletown Brewery) raised a mortgage on it