Melf's Minute Meteors plus some source of Temp HP should make things very easily survivable, if still somewhat painful, and give you 6 small fireball-like effects per 3rd-level spell slot.
If you want to go fully non-damaging (like druid faerie fire), a wizard could help out with other non-damaging spells like Pyrotechnics (2nd lvl, con save to avoid blinded for a turn). Makes flight-into-terrain possible, depending on how upset the Griffon's other senses are, especially balance / sense of up and down. Could certainly help birds + riders get used to flying in battle conditions with spells going off near them. Color Spray (1st) is somewhat similar but too short range (only 15 ft).
Other useful non-damaging spells to train saving throws with:
- Earthbind (2nd) to train in resisting that spell; definitely something you want flyers to prepare for when training to go up against spell casters.
- Cause Fear (1st) - 60 ft range, single target. wis save repeated until success (concentration, 1 min)
- Tasha's Hideous Laughter (1st) - 30 ft range, Wis save or fall prone / incapacitated.
- Gust of Wind (2nd) to create adverse flying conditions: 60 ft long, 10 ft wide line of wind from the caster. Str save or be pushed backward if you start your turn in it. (Or Warding Wind (2nd) if you want to buzz past a levitating or flying wizard.)
- Hold Person (2nd) on the riders only - Wis save.
- Ray of Enfeeblement (2nd) 60 ft range, Con save every turn until successful (1 min concentration). Mechanically, no ill effects except for reduced attack damage. But you could rule that it makes it tiring to fly, or harder to hold on under other adverse conditions if you combine effects.
- Fear (3rd) 30 ft cone, Wis save until success (conc. 1 min), unlimited creatures.
- Hypnotic Pattern (3rd) to train is Wis saves. (incapacitate / speed 0, so you need falling protection unless someone can "shake the creature awake" before hitting the ground.)
- Sleet Storm (3rd) 20 ft tall, 40 ft radius cylinder centered within range=120ft. Dex save or fall prone because of the ground being "covered with slick ice". DM ruling on whether this has a mechanical effect on fliers, e.g. riders maybe slipping off their mounts? It's at least adverse conditions to spring on your trainees at least once.
- Stinking Cloud (3rd) Con save against poison to lose your action "retching and reeling"
- Slow (3rd) - 6 creatures with one cast, AoE Wis saves repeated until success (1 min conc.)
- Storm Sphere (4th) - 20 ft radius sphere, 60 ft range, Str save to avoid 2d6 bludgeoning. Sounds awesome, and flying through the wind can be good training to stay on the Griffon. (Concentration for 1 minute, can use a bonus action to shoot lighting 60 ft, attack roll for 4d6 on hit. This part can train their dex?)
- Skywrite (rit. 2nd) to create a harmless "obstacle" course
- Message (cantrip) to help with communication between instructors and riders.
- Feather Fall (1st) to spare the rider's rings (which are single-use magic items).
- I stopped looking after 4th level wizard spells.
A Levitating or Flying wizard could cast these from some height, making the shorter-range effects useful for training without having to fly quite close to the ground.
An 18th level wizard can prepare any 1st and 2nd level wizard spells as their "spell mastery" slot to cast it at will. Takes 8 hours to re-spec this, but one very high level wizard can give many Griffon riders a full day's training against non-damaging effects. (Their save DC will be really difficult unless something temporarily reduces their Int without stopping them from casting spells...)
There are also less-damaging-than-fireball spells, notably the 2nd-level AoE low-budget fireball spells.
Aganazzar's Scorcher (2nd) only 30 ft line :( 3d8 fire, dex for half
Snilloc's Snowball Swarm (2nd) 90 ft range, only 5ft radius, 3d6 cold, dex save for half.
Shatter (2nd) is a Con save for half of 3d8 Thunder. (60 ft range, 10 ft radius)
Ice Knife (1st) bursts for AoE damage (hit or miss on the initial attack roll), dex save for half.
Melf's Minute Meteors (3rd) - 6 tiny fireballs with one cast: 120 ft range, 5ft burst radius, only 2d6 fire, dex save for half. You send them one or two per round, concentration for 10mins.
There are some cheapish ways to grant temporary HP, like a Shepherd Druid's bear spirit totem (AoE 5+druid level upon placing it, unlimited number of creatures within 30ft radius of it. Only once per rest, though.) Or spells like Heroism could refresh to 5 temp HP every round for a minute. (Concentration from a Bard of Paladin). Inspiring Leader can give level+cha mod temp HP to up to 6 creatures who spend 10 minutes listening to their drill sergeant / instructor. But the limit on repeated use is on the creature receiving the temp HP: one high-level instructor can repeat their speech to a new flight of cadets every 10 minutes. Aid will also raise 3 creature's actual max HP. (A Wizard can't do this part, but you'll want someone around anyway with Healing Word prepped.)
If it's possible to temporarily lower the Wizard's HP, that would lower the save DC, making it easier for rookies to get started dodging something. However, it might be better training to learn what it feel like to dodge a difficult spell, e.g. via Bless and/or Bardic Inspiration. (Note that Enhance Ability only helps with ability checks, not saves.)
As suggested by others in comments, having a healer or two on the ground with Healing Word is a good idea (1st level, 60 ft range, bonus action so you can move + dash + healing word).
Or a Circle of Dreams druids with Balm of the Summer Court (2nd level): 120 ft range, number of uses per long rest = druid level (if you only use 1d6 at a time). It's not a spell so presumably you could do it while wildshaped into something fast, like a giant eagle, without needing to be 18th level to cast spells in beast form.
Possibly a Grave Cleric for 30 ft range Spare the Dying in case of accidents.