I've not found an English travel journal yet, but Captain Trivier took about seven weeks from France in 1887.
This is an account of Captain Trivier's trip to Congo in the late 1880s.
He left France on August 20, 1888 (port not given) in the steamer Nerthe, and arrived in Dakar, Senegal in the evening of August 29, after a voyage stopping at three ports in Spain (Coruña, Ferrol, Vigo) and one in Portugal (Lisbon).
He then left Dakar on September 4 in the steamer Cameroon, and arrived in Libreville, Gabon on September 29, after stops in Sierra Leone (port not mentioned), Liberia (Monrovia, Grand Sester, Cap des Palmes), Ghana (Accra), Nigeria (Bonny, Calabar) and Equatorial Guinea (Malabo).
I can't tell if he took a third steamer or if the Cameroon continued, but he left Libreville on October 29 and arrived in Loango, Republic of Congo on November 9, after three stops in Gabon (Cape Lopez, Setté Cama, Mayumba).
This is a letter written 1887 and published in The Journal of the Manchester Geographical Society. It implies that Banana was the main port for steamers coming from Europe and West Africa, and gives you the route from Banana to Boma by local steamer in 1887; about a seven- to nine-hour trip.
To find more Victorian travel journals like this, I recommend you search in google books, limiting the time period to the 19th century (or a narrower time) with the keyword "journey" (plus Boma, M'Boma or Embomma, or even steamer) - a very common word in the title of travel diaries. Example search:
In French, the keywords would be "voyage" (=journey) and "vapeur" (=steamer):