To solve that problem, Kinslayer, you could simply have a 'statute of limitations'. Once the king was dead a week (or fortnight) could be set aside as a time of mourning for their lost ruler. If the culprit is not discovered by the end of that time, then they are able to come forward, and, allowing that they can prove they did it, are elevated to ruler ship. Of course, if this was the case then anyone that killed the king would leave very specific circumstances (a broken rose found between the deceased's teeth, a shard of glass wedged up his nose, etc.) so as to be able to prove that they were the perpetrator.