A google search for 'free trees nicosia' brought me to this page: Nicosia Municipality
"The Service responds positively to any citizen that requests to plant a tree outside his / her house. It supplies and plants the appropriate tree free of charge. The citizen's only obligation is to irrigate and protect the tree. The Service attends the trees and does not allow their destruction without the Municipality's consent."
The Department of Forests website is here: Department of Forests - Home Page
I didn't see anything about free trees so it would be best to call them to see. I know they sell pine trees around Christmas time from their location opposite Athalassa Park. They also have an office near the Municipal Swimming Pool so not sure which place you'd need to go to if they do indeed offer free trees.