Bump
Probably too late for you but maybe will help someone else, it's the "Blue Lagoon kosher hotel", located relatively farther out near the "Tombs of the kings" (which apparently are not kings), the hotel is
very family friendly, has rooms fully equipped with all the appliances you would need, washing machine, full size fridge, microwave, stovetop, dish washer, toaster. The rooms themselves were clean, the other sections of the hotel were less impressive, the food was pretty mediocore, the dining room kind of dirty, the pool also seemed kinda falling apart. There is a shul with regular minyanim at least in peak season.
In terms of location, it's pretty close to some of the archaeology and right on the water, they organize a number of activities out of the hotel, there is not much kosher food available although items are pretty cheap, you can buy fruits vegetables etc. There is a bus from the airport but it's pretty unreliable and takes a long time, if you want to maximize time get "bolt" and order a 30 Euro cab, the bus is only 1.5 for adult and 50% for kid but as noted shows up occasionally unrelated to schedule. There are a LOT of Israelis in Paphos and the hotel actually has all the signs in Hebrew.
All in all, can be great for a family the rooms are great the rest is more like a 3 start hotel. The location is very chilled, airport is small and easy to navigate, has a small but nice lounge for PP.