"But now we've got sixpenny steamers" - steamers began carrying passengers on the Tyne in 1818
[Ref: Lewenhak, Sheila. Steamships and Shipbuilders of the Industrial Revolution]

The "drops" carried the railways to river's edge and cut out the need for the keel boats that had previously carried coal to the ships.

"There's nothing gans now but a hyke in the new omnibus" - May be a reference to the Steam coach discussed in by Joshua Richardson in his Observation on the Proposed Railway from Newcastle Upon Tyne to North Shields published in 1834

"When the choice is between paying one shilling and sixpence to go from Newcastle to Shields by a gig or coach in an hour and a quarter or half, and paying sixpence to go from Newcastle to Shields by a steam coach in the same space of time that a tradesman is occupied in walking from his house in the suburbs to his office in the middle or lower part of the town, it is not difficult to anticipate how the public will decide. This observation is applicable with equal or greater force to Steam Packets.
When it is known that sixpence is the fare by the Steamer, which will be an hour and a half in performing the journey, and may be two, or even three hours, and sixpence is the fare by the Steam Coach, which will certainly not be more than twenty minutes on the way, it is quite clear how the community will make their election. If this is obvious in the most favourable weather, it is still more evident in stormy, wet, and cold weather. The only competition to fear would be another Railway, and even then, as appears from the number of passengers, the proprietors could have no reason to apprehend that they would receive less than sufficient to pay good interest for the capital invested."

William Rouse was granted a publican's license for the Steam Coach Inn at Newcastle in June 1839 and 1840.  He was granted a license for the Steam Carriage Inn on the corner of Perkins and King Street, Newcastle in 1841, 1842. In 1843 William Rouse did not apply for a license for the Steam Carriage Inn which was to be shut however he was granted a license for his new house, under the sign of the Newcastle Inn in Hunter Street, Newcastle in 1843. Perhaps the steam carriages had stopped running by 1843
[Ref: https://www.jenwilletts.com/steam_carriage_inn_newcastle.htm]

See also bar564 ~ Newcastle and North Shields Railway and bar273 ~ Newcastle and Shields Railway.

"And this is a' duin by one Grainger - a perfect Goliah  [sic] in bricks" - Grainger Market opened in October 1835. [http://www.ejr.ndo.co.uk/grainger.html] so this is the earliest date for the song.