There are a dozen constellations with no star brighter than +4.0 magnitude. Many of them are deep in the southern sky. They are:
ANTLIA, the Air Pump
Brightest Star: Alpha Antliae, apparent visual magnitude +4.25

CAELUM, the Engraving Tool
Brightest Star: Alpha Caeli, apparent visual magnitude +4.45

CAMELOPARDALIS, the Giraffe
Brightest Star: Beta Camelopardalis, apparent visual magnitude +4.02

CHAMAELEON, the Chameleon
Brightest Star: Alpha Chamaeleontis, apparent visual magnitude +4.047

COMA BERENICES, Berenice’s Hair
Brightest Star: Beta Comae Berenices, apparent visual magnitude +4.25

CORONA AUSTRALIS, the Southern Crown
Brightest Star: Meridiana, apparent visual magnitude +4.087

MENSA, the Table Mountain
Brightest Star: Alpha Mensae, apparent visual magnitude +5.09

MICROSCOPIUM, the Microscope
Brightest Star: Gamma Microscopii, apparent visual magnitude +4.654

NORMA, the Carpenter’s Square
Brightest Star: Gamma2 Normae, apparent visual magnitude +4.02

SCULPTOR, the Sculptor
Brightest Star: Alpha Sculptoris, apparent visual magnitude +4.27

SEXTANS, the Sextant
Brightest Star: Alpha Sextantis, apparent visual magnitude +4.49

VULPECULA, the Fox
Brightest Star: Anser, apparent visual magnitude +4.45
