The Brighton railway did not open until 1840 [i] so the reference must be to a steam coach. This is supported by "all the baiting a coach will require" later in the verse.
The Era was an 18-seater built in 1832 for the London and Brighton Steam Carriage Co
References:
[i] https://en.wikipedia.org/wiki/Brighton_railway_station (accessed 23May21)
[ii] Graces Guide to British Industrial History https://gracesguide.co.uk/London_and_Brighton_Steam_Carriage_Co (accessed 23May21)