Good question and the caveat will be who becomes available and price. Some options may be (just looking at lower seated teams):
Centers: Kadri, Monahan, Zibanajad, Pinto
Wing: Mantha, Lafreniere, Holloway, Kyrou
You mentioned both Kadri and Kyrou. Kadri would actually be towards the top of my center list, Kyrou is a risk but I think (based on nothing by opinion) that he will turn things around - high risk though so I'd move him down the list a bit. Mantha, Laf and Holloway I think would be strong additions and I feel remain underrated. As others have mentioned, Mantha may have too high of value currently due to his strong season.
Pettersson, as you mentioned, is enticing. Chances are he can turn things around and get back to the production he has shown in the past. He would also be a good replacement for Kopi, when he retires. The term and AAV are scary, but not overly so given his talent. The locker room / teammate situation is the biggest concern for me which I do not know how to properly assess.
There have been rumors going back the last season+ that the NYR's were interested in moving Zibanajad, but the asking price would likely be high. Not sure what Pinto's true upside is, but he is a solid Center who likely falls into a 3rd line center role on most teams. Good thing is that he is still relatively young and could at least fill the spot until the Kings develop a prospect to take over the role. Monahan simply has good value to contract and high experience.