Best Green Reinhardt/Bow Counter?

Of those units, FRobin is probably the best if you're looking for something well rounded for both player phase and enemy phase. Fae works really well with a bit of investment, and Bike/Hector are both amazing for their own reasons but BLyn can give them some issues. Nino is extremely potent, but mostly as a bladetome nuker. Long story short, I'd probably invest into FRobin as she performs very consistently.

Boey and Fae both work wonders. Without a Raven tome, Boey will probably die to Rein though.

Cecilia has the advantage of being a native Raven user, which reduces the cost of building her. I like her too much as a Blade Cavalry though.

Now you should run calcs to see if they can survive a hit from both of those threats in the same turn.

BIke can survive them but won't kill them in return, which is kind of a mistake (particularly if there is a dancer involved)

Same for Hector

Nino has to weak defenses to run a Raven build. And when she is running gronnblade, she can't survive Lyn, sometimes depending on their respective builds she won't survive Rein either.
Soren is a sub-Nino to me. Same kind of stat spread, only inferior. He won't survive BLyn anyway.

I don't really like FRobin ... Can't really explain why. But she seems to have very, very low stats to me. Mine is only 4Stars so maybe I'm mistaken about her. But she never worked for me as a Rein counter anywhere I used her.
Things might be different with a Raven + TA ... But others run the build better IMO

F Robin. TA Raven tome, Bowbreaker, Distance Def 3 seal. Probably want Panic Ploy on an ally to maybe be able to negate a Hone Cav on at least one of the two. The other slots are up to you. Allies with Fortify Res or Def can help as well. Unfortunately, that leaves F Robin unable to help against many other units than these two meta dominant units, so her versatility gets shot a little bit.

TARavenQRFrobin (Personal investment), followed by Fae, I think.

Tricolor raven tome Boey is why I bring Elincia.

As others have suggested, Female Robin is just an absolute beast against the current Lynhardt meta. Even a 4 star version of her can dumpster +10 Bowlyn with the TA3/Raventome/Bowbreaker set. Some people prefer Boey as you're not constrained by her being locked behind a GHB, and she's the only source of Blue Tomebreaker atm so you can't really afford to merge her.

Julia is actually an interesting option going forward though. With the new Distant Defense seal, she can become practically immortal against blue mages, and her high inherent attack power makes her good for one-shotting targets.

Fae + Distant Defense + Distant Defense Seal + Fortify Dragons + Quick Riposte has the potential to sit around 50 defense and 50 res, making attacking her with most non-red ranged units suicidal (Julia can't even kill through that without work). But that's a bit of an investment, and Nowi is probably slightly better. Also, -Res is maybe her worst bane as it's a 4 point hit to her resistance, and she's meant to be a mage tank.

Green is my favorite color, especially for mages. Currently, I run Nino, Sonya, Julia, Soren, Cecilia, and Boey. Eventually I'll probably try to make Merric work.

Julia +HP/-RES: She's a great mage duelist, especially with G Tomebreaker, but won't stand up well to arrows even with Raven unless she's +DEF. It's been awhile since I ran the calculations but, IIRC, 18 defense was an important threshold against certain Brave Lyn builds.

Boey +HP/-DEF: Those are terrible IVs...but he'd still function well with TA/Raven. 29 Defense boosted by TA is more than sufficient.

Soren +SPD/-DEF: Same as Julia but more so at -DEF. I'd recommend building him as a mage duelist with G Tomebreaker and using someone else to go against archers.

Cecilia +ATK/-SPD / Neutral / -HP/-DEF: All would do well but +ATK is probably the best. She's the budget option so you can try her out first to get Gronnraven+ and then use her for inheritance if it's not working out. Of course she's the best option for a cavalry team.

Hector Neutral: If memory serves, certain Reinhardt and Brave Lyn builds can ORKO neutral Hector. The upgraded Distant Defense seal might change this but he's not the best counter since he can't KO Brave Lyn on the counter (giving a dancer the opportunity to send her off to kill another unit).

Fae +DEF/-RES: She can counter both of them some of the time, one of them all the time, but not both of them all the time. Basically, unless she specializes some of the most optimized builds will get around her...but unlike TA/Raven she can't specialize against both at the same time. Essentially, she'll probably survive but may not counter which leaves your team vulnerable to dancer support.

Nino +Spd/Def: She'll have trouble with Reinhardt unless running something that boosts her resistance (like Fury) and will instantly die to Brave Lyn. +DEF Nino can make a surprise TA/Raven user but keep the blade tome with -DEF.

FRobin Neutral: Her stats are identical to M!Robin so she'll be just as good as he is...but with a better color.

B!Ike Neutral: He can survive both with ease pretty much out of the box but, like Hector, he doesn't KO on the counter which leaves your team vulnerable to dancer support.

Cecilia is an absolute monster with Gronraven, TA, and Green Tomebreaker. Just a fantastic utility unit who will work well in and out of cavalry comps.

Second vote would be for your Fae, although you may have to run TA on a -Res version of her to tank Reinhardt (don't know for sure) if that matters to you.

Hector and B!Ike are fine choices as well.

Julia laughs off Reinhardt but is physically squishy. Boey and Soren are simply outclassed by the other options IMO.

Nino is a monster player phase nuke; but she's not going to give you the bow coverage you want.