First, the easier way to do this is to use rsync in the first place.
rsync -avh --progress sourceDirectory destinationDirectory
However, sometime you think cp will be quick and you already kicked it off. Here is a quick way to check the progress of a copy command after you've already started.
watch lsof -p`pgrep -x cp`
This will let you know what it is transferring and how much it has left to do. In a way it provides a way to check the progress of the cp, copy comand.
To find out more check out these two SO links: