First off, check @Aceyfacey 's explanation how he’s managing to decline missions he doens’t like :
He doesn’t mention it, but you can also run epic arcs to bolster your faction standings w/o taking negative impacts towards the other factions.
Also, NPC agents usually cluster in pockets, i.e. other NPCs of the same faction will be closeby. If one Agent gives you a poor mission, and your deny cooldown is active, travel to the next one. The Isenairos Pocket (i.e. Solar Systems around Isenairos), for example. has many lvl4 security agents of corporations that are part of the Caldari faction, all within 2 jumps of each other, making it a popular missioning area.
Missioners playing eve the right way, use so called mission pullers: You put multiple alt capsuleers into your missioning stage station, and instead of attempting to go to another station and check whether the NPCs there give you better missions, you alt-tab to the next client, and check whether the other alt can get a better mission. If it can, the alt capsuleer “pulls” the mission, and the main runs it.
In most situations, you want to create a fleet consisting of your mission runner and the puller alt(s), which will cause the agent and corporation standings gains, as well as the corporation LP, to be shared among both, which is handy in case your pullers lack standings with some corporation, in which case you can powerlevel your puller with the runner. If the puller denies a mission, only the puller will suffer a standings hit, while the standings gain will be shared among the puller(s) and the runner(s). Faction standing gains are never shared, with the exception of the epic arc final mission rewards.
Of cause, the two techniques can be combined, in case the puller gets poor missions, too, and alt tabbing to other pullers yields only in more poor mission provisions until you find our you weren’t playing eve in a sufficiently good way, i.e. you ran out of alts before you ran out of poor mission offers.