I think having decent killing skills mostly overrides the need of diplo skills. What kind of diplo skills even exist? Don't piss off everyone (unless you can) and that's about it.
Not Diplo in terms of pissing people off, Diplo more on stopping one civ vassalling others, while your armies are targetting another civ.
Basically what happened was I had conquered my Continent, and Dutch, India, Maya, and Sally on another continent. I was cuirs rushing Willem, but while I was doing that Sally vassaled Pacal and Gandhi. When I went for Gandhi after vassalling Willem, I ran into several Huge 20+ stacks of heavily promoted Saladin Elephants and Camal Archers, which tore a lot of units out of my army (I was killing 2 for 1, but considering I was having to deal with this, and Ghandi longbows as well), even wilth 40+ units, and a train of others coming on ships, I just lost too many to conquer quickly enough. I did get Cav's and took a few more Indian cities, but Sally had 12 cities, and I needed to go through India to get to him, and by the time I got to him, Pacal had also teched Rifles, traded it to Sally, so now I had stacks of Rifles I was coming up on...
I now have Cannons, and they don't so I can start again, but having to change from building Cav's to Cannons has slowed me down somewhat, also Pacal had Statue of Zeus, so I had a ton of War unhappiness which I had not planned for.
I have 10 turns of Peace now, about 30 Cannons, and I should only need to take 2 cities to break Pacal out from Sally, and then it should get easier, but what seemed a simple Cuirs rush turned into a large slog, all because I did not bribe Sally off Pacal at the correct time to stop him Vassalling (too focused on Willem and keeping the others happy). I also killed most of Sallys stacks as well, so I think the war is probably won, but it should have been won like 50 turns ago if I had bribed Sally at the right time.
Anyway thats another game, won't happen here I don't think, as this map is a Pangea, and I won't be stuck ferrying around large amounts of troops