Considering that her plants do not scale with AP Mpen is an ideal route, The combination of rylai liandries is good. For raw damage output Void Staff Deathcap does the most to champions but doesnt increase your tankiness or utility.
Cdr doesnt seem to be that strong of a stat on zyra mid considering the passive and you should be getting most if not all the blues because soloing it is easy with plants tanking most hits. But if youre not getting blue like if your jungler is Eve or another CDR using mage then an athenes would help to mitigate the Blue absence.
zyra is a long range utilty champ that is quite mana hungry. so i suggest getting a tear on her cuz she so spammy. then boots then rush death cap. i dont recommend cdr on her at all cuz she get passive cdr from her plants. rylais and liandry's are really good on her becuase ur plants procs both of them. hg is amust on her though if they ahve a dive comp. you ahve no escape and that statis is just amazing, just make sure u drop ur spells first before u statis.
well i think cdr is a great stat for zyra,specialy cuz needs her ult a lot so i start with a doran's ring and if im getting feed,i buy a death cap and boots and rush to my athene's unholy grail, then i buy a rilay for better chasing ability and for durability,a liandry's torment for more dmg and MRpen ,i sell my doran's and buy a lich bane and my last iten depends on my situation,if i need more dmg i buy a void staff,if i need physical resistance i buy a zhonya's or a abyssal scepter if magical resistance is required.
remember that athene's most be one of 3 itens i buy first in early game,cuz of it massive mana regen and cdr which are very important stats for zyra
Your first big item should be Athene's, not tear. Maybe she have 20% CDR from W but you need achieve CDR cap to spam more abilities. Not to mention, Athene brings MRes (nice for mid champ) huge mana regen and 20% CDR. Athene allows you to be threat in all game stages while tear just disable your early entirely. And for boots you should go for Sorcerers.
In case of further itemization... buy rylai and don't even think about RoA when comes to hp necessity. Rabadon and Liandry's are your "must have". No need for descrption "Why you need Rabadon" but Liandry becomes your core because saplings applies passives entirely (when it's E sapling is apply even harder). Last item is purely situational but I suggest Zhonya as last item. Why? Launch your spells/saplings. When they charge on you just launch Zhonya and wait till saplings make their job.
Anyone who recommends building something besides Liandry's on Zyra has obviously never built one on her. Zyra's plants proc Liandry's allowing her to burst even tanks from from 50-0 if even and tanks from 75-0 if fed, her melee plants slow allowing them to automatically apply the double damage proc. For mana issues and CDR morellonomicon is the goto item. Starting item (for mid lane) should be faerie charm, and whatever combination of ward/pots you like. First item is kages, followed by haunting guise for lane dominance or sorc shoes for roaming then finish the other pen item(shoes if you got guise, guise if you got shoes). If you have blue control you can rush liandry's if not go ahead straight for morellonomicon.
If you are being bursted too quickly you can buy a giants belt for the rylais you will eventually be building however I find this is more related to playstyle. Remember your role is to land bind, drop your plants, then run BACK OUT. POP back into the fight as your Q comes off of CD, if you are dying you are probably just playing poorly or being focused. Being focused on zyra is actually okay...just make sure to get your combo off on 3+ people and land your passive.
Core Build is Sorc shoes, Liandry's, morellonomicon, Rylais...Finishing items would be abyssal/zhonya's (team dependant) and personal preferance. You already have a TON of magic pen so a void staff is pretty overkill unless everyone on their team is stacking negatrons....at which point it is GG anyways since your ADC is going to kill them all
For the Athenes VS Morellonomicon. Athenes does give more mana true...However Morello's costs less gold (600 less) builds out of a gp10, has the same CDR, offers the healing reduction that WILL help you kill people like voli/singed/ADC's and the mana should be a null issue since you have blue buff and should be backing often anyways. Buy some blue pots if you find yourself out of mana all the time.
Harass by putting ranged plants just behind the caster minions...they will often auto attack your opponent and hit harder then you expect.
ROAM. Landing a bind with melee plants is almost a 100% kill or flash if the lane can follow up. Make sure to ping BEFORE go to their lane and BEFORE you actually go in.
Due to the way jungle aggro works you can use your plants to tank dragon. This is good and bad, if you have a high damage jungle put your plants close to dragon to tank for him...tanky jungler? put them further away to maximize your damage