Increase Q base damage and make it slow. Reduce the speed of the cast animation to compensate for the stronger slow and damage. Have the QPlant do a small dot because QPlant usually only hits 1-3 times in lane and 1-6 times during a team fight before it is killed.
Change W passive from CDR to bonus flat Movement Speed when Q or EPlant hits a champion and 50% less bonus movement speed when hitting a minion or monster. Sort of like how Ahri's Q gives movement speed while in air. (Helps reposition in teamfights and scrims and promotes players to play with her plants and not stack zhonyas and instagibb with E or Q alone)
Reduce other spells base cooldowns by a second or two to compensate for losing the passive CDR.
W seeds lasts longer and can have more planted to make Zyra mid possible to be played with a plant in each lane bush and still able to use 1-3 empowered plants vs the enemy for poke.
Reduce E damage and increase projectile speed and reduce the max rank root duration and increase the rank 1 root duration. 1/1.125/1.250/1.375/1.5 (Should only be used for assistance to land Q and R. Shouldn't be a nuke.
Have his R have a faster animation ( not too much ) and have the damage only apply after the plant snaps. Because Zyra's style is locking down THEN doing damage. Hence CC buffs, and damage reworks.
Its a bit difficult, but if you are really interested, you can open a new window of Zyra here http://leagueoflegends.wikia.com/wiki/Zyra and compare the changes I made.
[Q]
ACTIVE: Zyra sprouts thorns at the target location after a 0.625-second delay, dealing magic damage to enemies within the area.
MAGIC DAMAGE: 70 / 110 / 145 / 180 / 225 (+ 70% AP)
RAMPANT GROWTH: If Deadly Bloom hits a seed, a Thorn Spitter grows and lasts for up to 10 seconds or until hit 5 times like a pink ward, attacking the nearest enemy with long-ranged attacks.
[W]
PASSIVE: Zyra gains a small burst of movement speed every time one of her plants auto attack, stacks up to 3 times.
Movement Speed Per Hit: ( 40 / 50 / 60 )/( 55 / 65 / 75 )/( 70 / 80 / 90 )/( 85 / 95 / 105 )/( 100 / 110 / 120 )
ACTIVE: Zyra plants a seed at the target location for 2 minutes, granting Sight icon sight of a small area around it. Up to 6 seeds can be planted at a time, and planting an additional seed destroys the oldest.
After 1.5 seconds, enemy champions can step on a seed to destroy it, but doing so grants True Sight icon true sight of them for 5 seconds.
If one of Zyra's basic abilities hits a seed, a plant grows from it and automatically attacks nearby enemies. Multiple plants striking the same target deal only half damage.
[E]
ACTIVE: Zyra sends a surge of vines in the target direction, dealing magic damage to enemies hit and Root icon rooting them for a short duration.
MAGIC DAMAGE: 40 / 90 / 120 / 150 / 175 (+ 30% AP)
ROOT DURATION: 1 / 1.125 / 1.250 / 1.375 / 1.5
RAMPANT GROWTH: If Grasping Roots hits a seed, a Vine Lasher grows from it and lasts for up to 10 seconds or when hit 5 times like a pink ward, attacking the nearest enemy with short-ranged attacks that Slow icon slow its target by 40% for 1 seconds.
[R]
ACTIVE: Zyra summons a monstrous thicket at the target location, slowing all enemies in the area as it extends. After 2.5 seconds, the vines snap upward, Airborne icon knocking up all enemies caught in the thicket for 1 second.
MAGIC DAMAGE: 180 / 265 / 350 (+ 70% AP)
RAMPANT GROWTH: Plants within the thicket are enraged and gain 70% bonus attack speed.