Caelum is an obscure constellation at the foot of Eridanus, and therefore only visible in equatorial or southern skies. It contains little of interest for binoculars. A good prerequisite study would be Eridanus.
Alpha Caeli is the brightest star in one of the most forlorn of constellations. The star is a double, with a very faint (13 mag) companion. To find the star, begin half-way down Eridanus. Gather together all the upsilon Eridani stars, now drop due south two full FOVs to find alpha Caeli and its neighbours.
Beta Caeli is due north of alpha, while gamma is northeast of beta. The only other Bayer stars (zeta and nu) are both 6th-mag, while the only variable of interest is R Caeli, found in the same FOV as beta.
R Caeli is a Mira-type long-period variable with a period of 391 days. It ranges from a very faint 13.7 to a brightness of 6.7, easily confirmed in binoculars.