The cypress was the most popular tree for Persian gardens. Roses also have a long history. Therefore, giving the cypress and the rose lets the poet avoid using a generic "tree" and "flower" and use archetypal garden plants.
For instance, Omar Khayyam made use of both
Iram indeed is gone with all his Rose,
And Jamshyd's Sev'n-ring'd Cup where no one knows;
But still a Ruby kindles in the Vine,
And many a Garden by the Water blows,
or
Perplext no more with Human or Divine,
To-morrow's tangle to the winds resign,
And lose your fingers in the tresses of
The Cypress--slender Minister of Wine.