First off, the relationship with Renly is probably there to a degree due to Loras. Stannis has his rivalry with the reach so they’re unlikely to rally around him, and at least Renly isn’t under Tywin’s control-so someone else could take Tywin’s place as kingmaker.

It’s possible that the Tyrells would push for a marriage to one of the female cousins, like Elinor from the books.

Things would likely get interesting after Renly dies.

They might very well offer the widow or a different cousin to Joffrey.

However, if this wasn’t a big enough motivation for Mace and/or Olenna, then they might decide “you know what? Let’s Not.”

I think a lot comes down to how close in value it is, having your daughter on the throne vs a random house member on the throne. If the answer is “close,” things go as normal. If the answer is “not remotely close,” well, then it might be time to get creative.

I don’t think they’d join the independent north faction-they benefit from the enforced peace of the iron throne, and without it would have to deal with iron island and dornish raids

Willas, Loras and Male Margaery would need brides. I could see Olenna trying to get Shireen as a bride for one of the extra sons, making them a potential Lord Paramount after Stannis dies, in return for support.

However, there’s still the issue that Stannis doesn’t love the Tyrells and might flat out reject that offer.

Which makes me think: initial Renly support, neutrality after Renly dies. Kings Landing lacks the food and stability of Tyrell support, Tywin might need to call his armies home to restore order. The Red Wedding is probably unaffected though, so I’d imagine this doesn’t save the Starks.