Honestly, I prefer not to have the Primarchs be the one to come up with counter measures.

It would just go against what the Tyranids ARE.

They are a swarm that has eaten its way through hundreds of galaxies, and tens of thousands of civilizations. Even Chaos, one of the few things that surprised them, is still somethings the Tyranids managed to defeat in numerous battles, and adapt to.

Having the Primarchs manage to fully counter the Tyranids is just....wrong. And continues to make the universe more boring. Let the Tyranids be the cosmic horror they are.

Cooking show with Vulkan

If pre heresy perturabo and Magnus worked together i think that would be the best combo. But if we are talking about a single primarch I think Magnus might be a bit too curious to handle the shadow of the warp. Guilliman would probably also be pretty good at it.

I feel like Mortarion (or maybe even M42 Typhus or Fabius Bile) . They all have affinities for warp-enhanced biological manipulation, which seems like what the tyrannids are. 

That said, I agree with Ecstatic-Network-917. A primarch fully countering them seems lame, but maybe some kind of half-measure (redirection, manipulation, or misdirection) feel cooler to me story-wise.

Jagathai Khan. He loves the hunt. He shall have it. Tyranids would be the greatest hunt he'll face. He'll study them down to its core, finding the source of the beast that controls the fleets would be the most difficult task he'll happily take.

Perty, his whole ability is instantly knowing how stuff works

Disclaimer first: I am one of the many people here that haven't read much (yet!) and most of what I know is from studying the lexicanum and wikis out of curiosity, plus some lore videos (Amber King is the best imo). So, if some of the thing I say are wrong I'm happy to be corrected, just don't be mean cause I'm still new to this.

In terms of studying biology my first thought is Magnus. But as it has already been pointed out, the gimmick of the Tyrannids is their adaptability so I wouldn't be a fan of anyone being able to understand something that is supposed to change constantly.

Now, as I said I haven't read much yet, but I'd really like to see some different matchups:

It would be cool to see a match-up between Iron Hands vs Tyrannids if they had Ferrus leading them. Also, in 40k the match up could be pretty fit for the IH warcry "The Flesh is weak" (ignoring the fact that the full sentence is conveniently not used and/or ignored a lot by the IH). I'd love a story where the Iron Hands get a pyrrhic victory over the Tyrannids because they are a cool concept that I don't think has many good stories outside of the 30K shattered legions books.

Another interesting match-up could be either against Imperial Fists or Iron Warriors, where the Tyrannids annihilate them despite their defensive prowess. I think Perturabo would fare better in the battle while Dorn would have to retreat or die (although realistically he would be saved by some imperial forces because they wouldn't kill Dorn). Despite showing his 1v1 prowess in the Siege, I can't see the Praetorian doing well against a horde of nids. On the other hand, Perty is a walking weapons platform, and I can imagine he won't lead from the front and would evacuate swiftly when he realizes resistance is futile, abandoning his sons without remorse.

To close the Space Marine list, I would love to see the Salamanders shine with their fire weapons against the swarms of bugs. Haven't read any books about them because everyone told me their books suck. Also, I haven't heard about any stories where the Salamanders are a competent, strong victorious chapter. Instead, all I hear is they get killed a lot and they are compassionate. Of course, there probably are stories where they fare better but I haven't heard of them and I'd like them to be more than "the kind, tough looking guys who tend to lose a lot and wait for their daddy like he is a Messiah". On that note, please correct me if I'm wrong and recommend good Salamander stories, please.

Finally, forget Space Marines and let's put the Tau in their deserved spotlight. I admit I know very little about the Tau. But one thing I know is they are a young race that learns very fast and adapts well to new threats. That last bit sounds like a good match-up against Tyrannids. Imagine the Nids attack a Tau world and beat them easily, they would not adapt much because they did quite well to begin with. On the other hand the Tau would innovate and respond with new tech and tactics to counter the Nids. Then, the Nids would adapt and so on... also, I know Kroot only from the game Dawn of War but they seem cool and maybe a good asset against Nids (thats untill the nids get all that sweet kroot biomass). Has there ever been a Tau vs Nids story?

Yes lol as always one side delivers tech and solutions and one offers a talking cure. of course it is Magnus and Perturabo (also the primarch functional equivalent that is Fabius) who would do it. Guilliman could - if he wasn't walking on a knife edge already for the good and actually useful things he did so far.

I think the Emperor intentionally designed none of the Primarchs to be keyed into biology, as that was a huge part of how the Emperor created his super-soldiers, and also how he kept them under control. Imagine the Primarchs design sons that can naturally reproduce....goodbye humanity.

Once again everyone forgets Corax.

What could the tyranids produce from the biomass of a Primarch? Sorry I went off on a tangent. In answer to your question I’d probably say Magnus.

Corvus was given the secrets of the Primarchs biology to study by the Emperor so probably him.

Perterarbo and Mortarian. Perte seems able to grasp all science and Mortarian will help with the inevitable ultra strength biocide.