For reference purposes: 
 *1. Daimler Conquest Saloon (1953–1956), 4/5 seater annnounced May 1953, 4 months after Bernard Docker (MD of BSA) made himself MD of Daimler, really a six-cylinder Lanchester Leda with a Daimler grille and probably had been meant to be sold as a 6 cyl. Lanchester 
 *2. Daimler Conquest Century Saloon (1954–1958), 4/5 seater announced March 1954, just a Conquest with the higher output engine originally for the slow or no selling Roadster 

 *3. Daimler Conquest Century Drophead Coupe (1954–1955), 4/5 seater (no, a genuine 4) a Conquest with its roof cut off and a soft top, probably done by Barker. It replaced in the catalogue the Barker Sports Special on the DB18 chassis (which was really replaced by the Barker Special Sports on the Regency chassis) 
 *4. Daimler Conquest Century New Drophead Coupe. 4 seater Dunno what was new about it but here's part one of our problem solved The Book refers to it (p271) as the Century Drophead and says it went out of production late in 1957 

 *5. Daimler Conquest Roadster (1953–1955) open two-seater with clip on sidescreens this is the Roadster announced October 1953 using what became the Century engine 
 *6. Daimler Conquest Roadster / Mark II Drophead Coupe open two seater / wind-up sidewindows and therefore a dhc or convertible,  a more civilised Roadster. I can find no useful info about this except it must have been forgotten by April 1959 when the Dart (became the SP250) was announced in April 1959 and that too, just the way the Roadster was at first, was Unbelievably crude. 

 The Whole Daimler Car Production for 1959 was 110 SP250s of which 77 went to USA 14 years earlier the workforce was 16,000 people. 

 (below written first before the table above but no matter) 
 ::::Ah, OK, I see some light. See the Flicker versions of the car rely on the wet-weather driver clipping on sidescreens as well as pulling up the hood - perhaps taking just ten minutes into the start of a Sydney downpour - its a VIC car I note - well I think what is probably the Mark II (in your three pictures) will have been in English classic parlance an all-weather car/drophead coupé. i.e. with wind-up side-windows and so in US parlance of the day a Convertible and genteel. That phrase drophead coupé has confused Seasalt (he only goes wrong in that one paragraph which you and I have both quoted) - and thereby you.  
 ::::Would you consider checking with your local library system and getting from it Daimler Century, the full history of Britain's oldest car maker, by Lord Montagu and David Burgess-Wise, foreword by HRH The Duke of Edinburgh, published by Patrick Stevens Limited 1995, ISBN 1 85260 494 8. 
 ::::For some reason the book does not tabulate models and variations and production figures. I guess this is because while they often had that info they were unable to find all of it but that's a guess. If you go to the index at the back and work from that it may become clearer to you though I must admit in this particular case my confidence comes from my memory of the events in the 1950s rather than that book. Anyway this is why I am being so slow and careful about amending the separate articles on individual Daimler models. This article is the first that I have taken more than a casual glance at.  

 ::::Does all this typing by me make you any more comfortable?