Well, that exceeded my expectations: thanks to all for those immediate and helpful responses.  Fantastic.  I get a clear message that the answer is “Ford Tri-motor”, with some real thoughtfulness along the way, and that is everything I could have hoped for.

I should offer that I wrote at the same time to some aircraft museums, and got the same clear “Ford Trimotor” judgement.  Brian Niklas at the Smithsonian’s National Air and Space Museum came right back with “Ford 5-AT Trimotor”, and Ian Richardson at the Yorkshire Air Museum in England also opted for the Ford Trimotor, then considered a Dornier model (unspecified) as a possible alternative, but then went back to the Ford Trimotor.

I had said that I had not wanted to prejudice views on what the aeroplane is, by setting out those previous, varying theories.  Let me offer those now:  

• At the time of the stamp issuance, philatelist Benjamin Hamilton Jr (who was at the time Research Advisor for the Consulate of Liberia in Los Angeles) noted that this first airmail service employed a CJC-5 Model WACO Cabin Monoplane loaned by the Firestone company, and – against, I would say, the evidence of his own eyes – asserted that this was what was shown on the stamp.  The Scott stamp dealer catalogue follows this “Waco airplane” label, as does Lothar von Saleski’s “Liberia Specialised Stamp Catalog”.
• The Sanabria catalogue of airmail stamps has said Fokker F-18, and this was echoed by Henry H. Rogers’ magisterial book “A Century of Liberian Philately”.
• The Minkus stamp company (now defunct) said in its catalogue “Ford Trimotor ‘Tin Goose’.”

I see that here user avion ancien questioned whether the stamp design really shows an actual, rather than imaginary trimotor design.  Excellent question.  John Webb had a 50-year career in the stamp business, ending up as Deputy Chairman of the Stanley Gibbons companies, but as a young man he designed just four sets of stamps: one for Mozambique (1937) and three for Liberia.  Two of those Liberian sets are known with certainty – this 1936 airmail design, and a 1937 set (also triangular) with animals and then-President Edwin Barclay – but it seems likely that a 1938 airmail set was also his design.  The designer of that set, interviewed at the time in Gibbons’ Stamp Monthly, said of the designs I attach here, “The flying boats of the remaining two designs are just typical modern machines and are not intended to represent any definite types.”  This is notwithstanding that Ben Hamilton, Jr. reported that one was a “Compagnie Aeromaritime Sikorsky amphibian hydroplane”.  However – tantalisingly – that designer is not named in the article (whereas Webb had been named with respect to the earlier designs, and had discussed how points in his design where he had deliberately been accurate/correct had then been changed in the final stamp).

While the Firestone connection and the WACO ‘plane are known for the first flight, the information from user 1batfastard about the more general connection between Harvey Firestone and Ford is great to have.  And the word from user Aerotony that the WACO ‘plane was replaced in the airmail service by a Ford Trimotor is very interesting – is there any chance that you could point to where you found that information, please?

Many thanks again.