Daryl's storyline on The Walking Dead is the most difficult to predict because he has no comic book counterpart to go off of. His presence in the show means any other comic storyline can be altered to accommodate him. His existence has already resulted in changes in the Negan storyline from the comics, which means going forward all bets are off. Anything could happen when it comes to Daryl. So will Daryl kill Negan on The Walking Dead Season 7?
As of right now, Daryl is in a unique position. He may be Negan's prisoner, but Negan's goal isn't simply to torture Daryl as punishment for his and Rick's actions. Negan likes Daryl and sees the value in him, so instead he wants to break Daryl enough to make him into one of Negan's own. He wants to convert Daryl to the side of the Saviors. Daryl is understandably not tempted by this offer given how fiercely loyal he is to his friends, but there are ways that he could use this to his advantage.
If he wanted to go undercover and pretend to join Negan's side, then he could easily earn a spot in Negan's inner circle. Then, when Negan's guard was down, Daryl could take him out. Daryl did prove himself adept at fitting in with a rough crowd when he briefly joined forces with the Claimers in Season 4.
Just to be clear: there is no guarantee that this could or would happen. It's all just speculation at the end of the day. However, in the trailer for "Service," Daryl can be spotted amongst the crowd of Saviors when Negan comes calling in Alexandria to grab supplies and do some general terrorizing. That could mean a few things. Though it's a very quick, there's a background glimpse of Daryl, who still looks worse for wear. It's possible Negan just brought him along on the field trip to remind Rick of the power Negan holds over him. Daryl definitely doesn't look like a team player in the clip; when the rest of the Saviors move on the town, Daryl remains perfectly still.
However, it would make sense for Daryl to eventually leverage his position to get some power back. Right now he's still grieving and coming to terms with what happened in the premiere. Based on where fans left Daryl, crying it out in "The Cell," it looks like a lot of his spark has been diffused by suffering. But that doesn't mean it will be gone forever.
After everything Negan has done, it would be poetic justice for Daryl to trick him by playing the part of a Savior only to stab him in the back later on. Fans can only hope that Daryl still has some tricks up his sleeve.