Think of who in a D&D PC sense would worship them, and use that.
For instance, God of Love...if she's popular amongst elves, then perhaps the Longbow is a choice weapon for her (Cupid's Arrow and all that). If she's mostly worshiped by commoners in the home, perhaps unarmed strike would work (love's gentle caress, or the slap of an offended woman). Or think of something euphamistically (there's a reason love deity = staff or club, after all...), or of possible other associations joining with their main portfolio (deities of love often have naturalistic/fertility inclinations...perhaps druids worship them, meaning a scimitar would be prefered?). Perhaps she's associated with families, and thus defense of the home, and thus homeland defenders would associate with her, and if they're heavily armored fighters, perhaps shields would be important, or if they're wild barbarians, perhaps greataxes would be favored. If she's the nonviolent type, bolas, nets, saps, etc...though I think having a deity of love favor the sap is just asking for that old joke...
(What's the best pick up line you've ever heard?
"Does this smell like chlorophorm to you?")
In another example, God of Wisdom. Age = Wisdom. When you get old you need a walking stick. So walking stick = wisdom. Walking stick can be reasonably extrapolated to quarterstaff.
As far as nessecity, keep in mind the deities in D&D were designed and presented with PC's in mind. They're all designed to be used by adventurers, and 95% of adventurers probably use a weapon of some sort (the exceptions being some monks, who *are* a weapon of some sort), and adventurers who worship a god like to often emulate much of their equipment after the god. Mechanically, all a favored weapon does is provide you some proficiency if you take the War domain, so if the deity doesn't offer the War domain, it's not mechanically essential at all. And if your adventurers prolly won't choose the god, it's not essential. You may want to help them out by including other important things to their deity, and having them come accross/find use for them....nothing delights a the worshiper of a god of wisdom quite like a potion of Owl's Wisdom, and a potion of Eagle's Splendor probably helps out a god of love a lot. It just won't include a weapon, which is probably okay.