You mention Conifers, so will suggest Leylandi. I know the first thing you may think is how big they get and many a neighbour dispuets have arose about them, but they are fast growing, so will cover well in a fair time.
The seccret is to let them grow to the height you want then cut the top and keep them at that height. This also encourages them to spread in width.
Another option is Russian vine (Fallopia). It is fast growing so will cover the fence quickly. Just keep in mind to keep it in check as it is also known as The Mile A Miniute Plant!
These are what I would consider.