The Sophie B. Hawkins song "Don't Stop Swaying" depicts a brother and sister who fall in love, from the sister's viewpoint. The implication is that they were abused or abandoned by their parents and turned to each other for comfort.
'Cry Little Sister' from The Lost Boys, by Gerard McMahon, is a love song from a brother to his sister. It may be incestuous or metaphorical but deep passion is implied (Temptation heat/beats like a drum/deep in your veins/I will not lie, little sister/come to your brother/unchain me sister/love is with your brother)
'Brother and Sister' by The Gun Club ends with (I am your brother, your lover, I give you my blood/I'll follow you anywhere)
Not uncommon as a theme in folk songs either; "Sheath & Knife" probably being one most easily listened to at the moment. Example modern lyrics.
Several Child ballads have this as a theme, actually; for instance, "Lizie Wan".
The song "Spiel mit Mir" by Rammstein is about incest between two siblings. The only one specified is that the song is addressed to 'brother' (given that the singer is male though, most people presume it's between two brothers rather than a brother and sister).
Possibly the Dashboard Confessional song "The Secret's in the Telling". Lyrics like 'we keep this secret in our blood' would, at least, seem to imply this trope.
SoundHorizon's song Ark, to a T. The song is told by the girl, who wants the brother to forget about their initial relation and be ignorant. Here it is with subtitles.
The Ghost Bee's Tear Tassle Ogre Heart, although it may be one-sided (on the sister's side).
In the song "Mary be Fair", a young man has a series of marriage prospects shot down by his father, who reveals that he fathered each of the girls during an affair. At the end, it turns out that it's ok, since the mother reveals that she'd been having an affair as well, so he isn't actually related to the girls after all.
This is a turnabout of the traditional original, where it's the girl who has the relationship problem with all the boys in town.
"Butterflies" by Sia sounds like a love song about a long relationship that's had many ups and downs, but ends with the lyric, "because we came from the same cocoon."
Have three guesses what the song "Geschwisterliebe" (German for "sibiling love") by Die Ärzte is rather explicit about.
In the Andy M. Stewart song "The Orphans' Wedding", a happy marriage is brutally interrupted when a government official informs husband and wife that that they are, in fact, siblings.
The line "You can fool with your brother, But don't mess with a missionary man" in the chorus of the Eurythmics song "Missionary Man" implies that the singer has at least had thoughts in that direction, whether or not she's actually done anything.
"Sister" by Prince. Apparently, incest is all it's cracked up to be.
Patti Smith's song Kimberley hints at an incestuous relationship between two sisters.
Heart's song Barracuda is an angry rebuttal of the rumour that Ann and Nancy Wilson were a lot closer than sisters should be. The Wilson Sisters were not amused to discover their own management and record company had deliberately spread the rumour to drum up interest and publicity.