Source: Ultimate Magic (see Binding Outsiders for further details.)
In general, one summons a genie for magical power or ancient wisdom. Genies seek and value power, though they are more brash and boastful than most. It is said the best way to secure the attentions of a genie is to speak its true name, and to offer it aid in battles against its political enemies—a wise conjurer researches the inner battles of geniekind before summoning a genie, or else is prepared to cow the genie with strong magic.
Efreeti: These warlike creatures value weapons with enhancement bonuses of at least +2 and scrolls of 4th-level or higher spells; these provide a +2 bonus on the binder’s Charisma check. Efreet also appreciate attractive humanoid slaves, which give a +1 bonus on the binder’s Charisma check for every 10 slaves offered.
Janni: The weakest of the genies, the jann are also proud and prone to insult. Gifts of rich fabrics, gems, or jewelry worth 1,000 gp or more soften their outlook and give the conjurer a +2 bonus on her Charisma check.
Marid: Capricious and unpredictable, marids love performance and art—providing them artwork worth 1,000 gp or playing a DC 30 Perform (any) piece (whether performed by the binder or his ally) piques their interest long enough for the conjurer to gain a +2 Charisma bonus.
Shaitan: As the most dense and brash of the genies, shaitans like games of chance and physical skill best of all. Should the caster offer services in exchange for a throw of the dice or a wrestling match—and go through with the offer—he’ll receive a +2 bonus on his Charisma check.