Palace of Spies, by Sarah Zettel (HMH Books for Young Readers, Nov. 2013), set in 1716, is the only one I can think of, and it sets a nicely high standard for this particular little sub-genre. This is a good period for intrigue and plotting--the newly installed Hanoverian king is not universally loved and the Jacobites (who want the Stuarts back) are plotting and seething. So basically, the palace of the Prince and Princess of Wales is a hotbed of somewhat more than your run-of-the-mill political and social tensions.
And young Peggy Fitzroy is right in the middle of it.
Peggy didn't have a choice. The mysterious friend of her deceased mother, who took her in when she was booted out of her previous guardian's house, plans for Peggy to take the place of Francesca, a young lady in waiting who left the court and died (mysteriously?) some time ago...and as no one at court knows she died, and Peggy looks somewhat like her (the fashions of this period--heavy makeup and powdered hair help viz disguise), Peggy can go to court and report back to her new guardian and his associates--a gentleman (?) of uncertain status who's a whiz at cards, and unfriendly woman who will be Peggy's maid.
And Peggy has no better alternative to offer herself. But no one has told her just what she's reporting on, and so Peggy, step by intricate step, finds herself ensnared in a dance of intrigue that is more complex than she had imagined. Francesca had secrets--a lover, a dream, a twisted past of her own--and Peggy gradually discovers that these secrets could be deadly.......
So it was rather fun, to see things getting more complicated, and trying to spot clues and figure things out! My only reservation is that the whole business of not actually giving Peggy any meaningful instructions--I never quite understood why her new guardian went to all the work to get Peggy installed as a lady-in-waiting if he wasn't going to use her in any useful capacity, and this felt like a pretty substantial plot hole to me. Some of his other actions made little sense to me either. But it's possible he was just making sure she was safely installed first, and didn't realize what a trap she was going to find herself in, and maybe the sequel will make things clearer-or even more murky and dangerous!
If you enjoy historical intrigue and mystery, give this one a try.
Something I liked: One of the characters is an artist's apprentice, so there are a few (not lots, but some) bonus bits about Georgian art thrown in.