There's a couple pesky puns in CDS #51, both based around characters misunderstanding homophones.
In the first one, Satori says Mizuchi is shiro ("white", innocent), to which Shinmyoumaru responds "Shiro? As in 'castle'?" That's a pretty nonsense sentence where the joke doesn't really go much beyond Shinmy being silly - to give her some credit, Satori's words could maybe have been taken as "She's going to the castle" or something - so, obviously unable to come up with a very close equivalent, I ended up just replacing it with a different, less punny misunderstanding that I think at least fits in pretty naturally.
With Raiko, the original joke is that she confuses onryou as in "vengeful spirit" (怨霊) with onryou as in "sound level" (音量). Presumably Seija said something like "I'm here to talk about the onryou".
Partly because we don't actually see Seija say the original line, only Raiko's response to it, I decided that I didn't really have much room to play around with the "vengeful spirit" part and have Seija say something completely different and easier to pun. But obviously there's no applicable word that would sound like "vengeful spirit" in English, so instead, I just had Raiko think that vengeful spirit was referring to their rebel attitude as a tsukumogami rock band or something vague like that. You could say I just translated the whole scene very directly without even making it a pun, but at least it was intentional, not just me missing the joke or something.
In retrospect, I thought of the alternative of having Raiko say "...A warning?", but while that would've been pretty elegant too, I think it's more a sidegrade that changes the meaning of the dialogue quite significantly and makes it less funny (?) rather than a clear upgrade.
Bonus mention: Apparently the story arc names are all incorporating the games' Japanese titles now, albeit in these two cases they're also the names of locations. Ten Desires' Japanese title is 神霊廟 ("Divine Spirit Mausoleum"), while Double Dealing Character is 輝針城 ("Shining Needle Castle").
Trying to replicate this effect in English, assuming I'd even realized from the get-go that it was going to be a trend, would've required me to come up with some completely homebrew puns involving Ten Desires and Double Dealing Character, without even knowing what was going to happen in the story. Judge for yourself if you really wish I'd done that. Hence I've just been translating them very literally.
(The reason the first one is missing the word "spirit" is that it's actually part of the word "mausoleum" 霊廟).
Looking forward to how they squeeze LoLK's 紺珠伝 ("Ultramarine Orb Tale") into a chapter title. My guess is some reference to the Earth as a blue orb.