Maybe use superstition.
There's a long history of superstition, luck-offerings, and other attempted bargains with the supernatural. None of these were sanctioned by the wealthy and powerful (especially not if there's a church who would not like competing with these superstitions), but they persisted even in the face of concerted opposition.
Most such offerings are small - a bowl of milk for the fae, salt over the shoulder to ward off bad luck, ribbons tied to a tree, sweet herbs offered to a fire, coins in wishing wells. The point is, though, the offerings would already be in the culture, a jumping-off point for the assassins to spread a...certain story. After all, given the idea of small offerings for luck, why not big offerings for assisted luck - especially if or when words gets around that this offering, this story, seems to work.
So, now to make it work.
Someone might, if they were looking for a little extra luck, give an offering to a wishing-well (or cursing-pond, who wants to dive into a well) and speak their wish aloud. The "water spirit" won't take a direct hand unless the coins one is offering are gold, though.
One heard that there's a little old shrine in the woods, there. If a person had an obstacle in their path, one would go to the flat topped stone, bury an offering of coins there and lay a token closely representing their target on the flat stone, and the obstacle will meet an unfortunate end.
There's a wishing tree down that trail, old and gnarled, and folk will tie offerings on the branches with their written request, and coins, tucked inside the pouch. If one offers a generous handful of silver, the tree sprites may offer the very worst luck to one's foes.
Or, well, any small tale like that.
The assassins would keep a watch - maybe even use it as a training exercise, or punishment, since it might be boring - and so they would see who is offering, and who they want removed, and can immediately grab the offering and make sure it's enough. Additionally, if there's some confusion about what was requested for some reason, there's the fact they will likely know the local gossip, and therefore can figure out who they are being asked to target, or else the use of a written request (rich enough to hire an assassin can mans can leave a name in a note) or a token absolutely identifying the target. And if all else fails, or if the payment isn't enough, or anything else, they can slip a person in to negotiate with the one asking personally. After all, they know this person is interested already, don't they?
The story will need to be carefully written, when first started, so they don't get too many requests for, um, services not offered. Maybe make it known it's a cursing-place instead of a wishing-one or the spirits involved are dark and deadly, to keep the requests to death and mayhem instead of healing or other miracles. Also, they should have an idea of what to do if someone does offer a payment for something they can't or won't do, in mistaking the process for a genuine spirit offering - maybe returning it, unseen, to the one asking would be both an impressive proof that someone was listening, and underlining that not all bargains will be accepted.
But after a while, it will become a set routine. People will know what they're asking for, and what they're getting, and what the price is. Customers found by other methods can be told this is how to get in touch for repeat business. There will be plenty of people attesting that this offering really works.
Maybe people will realize it's just a contact point, a dead drop, or maybe they will genuinely believe it's a spirit-thing - but either way this guild has got a contact point that does not lead back to them (since they can watch any potential customers and approach at their leisure).