Click here for more info on the East Empire Blessings and how convincing the Jarls works.
The following options are available for both Laila Law-Giver and Maven Black-Briar:
Regardless of who the Jarl is, killing Uerkeelern Cold-Blade will unlock the Favor option.
If Laila is the Jarl, the clue that this Favor option exists is a note called "Bounty from Laila Law-Giver". This can be found in the Mistveil Keep Barracks on a table.

If Maven is the Jarl, the clue is a note called "Note from Maven Black-Briar", which can be found on that same table.

The target can be found near the chamber with light beaming down on a stump with an axe stuck in it inside the Ratway.

Regardless of who the Jarl is, a note can be found on the nightstand next to their bed that will unlock the Coerce option. The note for Laila is called "Letter to Jarl Laila Law-Giver", and the one for Maven is called "Maven's Notes".
