If you allow two and a half hours you should be OK. It's motorway most of the way, but not as we know it! There's a series of roundabouts as you pass Limasol although they are currently building flyovers.
Watch out for the speed camaras too as I've heard that the points will go onto a UK licence as it's an EU Country

Paphos ...is a good two hour drive to the Eastern end of the island, and a very hot drive, my car AC is working but just not up to this heat wave we are enduring at the moment...dropping like dead flies here, while you are drowning..

Jim
Would certainly swop you weather at the moment!
I should be leaving Paphos around 17.00hrs so hopefully may be a bit cooler in Sept

Well if you were here right now you just may change your mind!!!

Whoops

it took me an hour and twenty minutes to get from near pissouri to ayia napa. Its all dual carriageway so you should be fine if you allow two hours.