I'm writing an adventure that features an Emyprean, who for story purposes would ideally be an offspring of Brandobaris. I'd like to know if there are any offspring of Brandobaris referenced in any of the Forgotten Realms lore. The answer need not be limited to 5th edition- if there are references from previous editions, novels or even other campaign settings, I'd like to take that into consideration.
Brandobaris has received very little treatment in D&D sourcebooks since Advanced Dungeons & Dragons 2nd Edition, being only briefly mentioned, if at all.
In AD&D 2e, however, the book Forgotten Realms: Demihuman Deities gives Brandobaris a fairly detailed biography. There we see:
Only Tymora regularly accompanies the Trickster on his jaunts, and Lady Luck and the Master of Stealth are said (by halflings) to be romantically linked.
Regarding Tymora, the AD&D 2e book Faiths & Avatars says:
She is reputed by sages to have had short-lived romances with several of the good male deities of Faerûn, but these ended amicably on both sides after a short while.
There is nothing explicitly mentioned about Brandobaris having any children in what is, to my knowledge, the most thorough biography he has ever received in a D&D sourcebook. The best we can do is say that the halfling people believe Brandobaris had something of a romantic trist with Tymora.
An Empyrean offspring resulting from such a relationship seems entirely plausible.
We also see the same lore expressed in 3e's Faiths and Pantheons, as outlined in Eddymage's Answer
The relation between Tymora and Brandobaris suggests so.
The latest information available (to the best of my knowledge) is its entry in the Faiths and Pantheons of the 3rd edition:
A rumored romantic dalliance with Tymora may be responsible for Brandobaris's legendary luck, which plays a central role in the countless tales of daring-do traded from halfling to halfling like currency at waystations across Faerun.
Tymora's entry in the same book says (page 78):
[...] she also retains much of Tyche's romantic fickleness - she's seduced dozen of deities and countless mortals, seldom staying with a single paramour for more than a year or two. She shares a somewhat casual, long-running romance with the halfling deity Brandobaris, whose passion for daring-do and ribald shenanigans rivals her own.
Thus, this casual relationship between the deities could have give birth to a child (or more?). Nonetheless, no official source clearly state this.
Actually, the name of Brandobaris is mentioned also in the 4th edition of the Forgotten Realms Campaign Setting (page 81), but it is only a name in a table.