I haven't seen anyone suggest this moveset yet so I'll just type it down. Keep in mind that this is a bit different from the usual movesets but if you want to try something new you can go for it.
Ability: Chlorophyll
EVs: 252 HP / 252 SAtk / 4 Def
Modest nature (+SAtk, - Atk)
- Sunny Day
- Solarbeam
- Sleep Powder
- Dream Eater
Explanation: Sunny Day and Solarbeam are a good combo and since Exeggutor has Chlorophyll its speed will be boosted. Sleep Powder is the highest accuracy sleep-inducing move and it goes well with Dream Eater, which has a high power (100) and also lets your Exeggutor gain back some health. The downside to this moveset it it takes some time to set-up, and your Exeggutor may not survive a SE move. Only use it when there's type effectiveness or Exeggutor will very likely be OHKO or THKO. Sunny Day and then Solarbeam or Sleep Powder and then Dream Eater.
Alternatives: If the Sleep Powder-Dream Eater duo doesn't sit well with you, maybe Psychic and Ancient Power can replace the two. Giga Drain can replace Solarbeam as well and if you really don't want to set-up, you may choose to replace Sunny Day with something else. So you will have: Psychic, Ancient Power, Giga Drain + Fourth Slot.