As per my earlier post, the F-Type Coupe roof is not engineered to support the weight and stress of a hard roof box and its contents. That is the information I've seen and I believe to be correct as JLR never intended it on this Luxury Sports Car. They didn’t provide the facility for roof bars probably because it would also spoil the car’s aesthetics (see screenshot below).
However, others have mentioned the suction method for attaching a roof box. The SeaSucker Monkey Bars roof rack system shown in the YouTube video posted earlier seemed to be successful on the Ferrari SF90? I haven't seen or heard of this being tried and tested on an F-Type Coupe so it's up to the OP to decide?
https://seasucker.eu/products/monkey-bars-2020-edition
Taken from the FAQ's section...
"We don’t recommend using our products on wrapped vehicles. Our testing shows that our vacuum cups will pull a bubble in the wrap when attached, which screws up the wrap and is not a safe attachment point for a SeaSucker. To make it work, some people have removed the wrap just where the vacuum mounts will sit on their vehicle.. However, you are absolutely able to use a SeaSucker rack on a ceramic coated car."
Furthermore, if you attach a roof box onto your car it can invalidate your insurance unless you declare it, due to it being a risk.
On a separate note and in regard to the previous post by member
Willieo, I've never seen pics of a Border Collie in an F-Type before!

He seems to have made himself very comfortable there. Hopefully he doesn't try cleaning the inside of the tailgate glass with his tongue or nose!