  A sample of 16 blue compact dwarf galaxies (BCDs) in the Virgo Cluster has
been imaged in the near-infrared (NIR) in $J$ and $K_s$ on the 2.1m telescope
at OAN-SPM in Mexico. Isophotes as faint as $\mu_J$ = 24 mag arcsec$^{-2}$ and
$\mu_{K_s}$ = 23 mag arcsec$^{-2}$ have been reached in most of the targets.
Surface brightness profiles can be fitted across the whole range of radii by
the sum of two components: a hyperbolic secant (sech) function, which is known
to fit the light profiles of dIs, and a Gaussian component, which quantifies
the starburst near the centre. Isophotal and total fitted NIR magnitudes have
been calculated, along with semimajor axes at $\mu_J$ = 23 mag arcsec$^{-2}$
and $\mu_{K_s}$ = 22 mag arcsec$^{-2}$. The diffuse underlying component and
the young starburst have been quantified using the profile fitting. Most color
profiles show a constant color, between $J-K_s$=0.7 to 0.9 mag. The diffuse
component represents the overwhelming majority of the NIR light for most BCDs,
the starburst enhancing the flux by less than about 0.3 mag. Linear
correlations were found between the sech scale length and the sech magnitude,
and between the sech semimajor axis and the sech magnitude. Overall, galaxies
with more luminous diffuse components are larger and brighter in the centre.
The central burst correlates with the diffuse component, with brighter BCDs
having stronger star-bursts, suggesting that more massive objects are forming
stars more efficiently. BCDs lie on the ``fundamental plane'' defined by dwarf
irregulars (dISs) in Paper I, following the same relation between sech absolute
magnitude, sech central surface brightness, and the hydrogen line-width
$W_{20}$, although the scatter is larger than for the dIs. [one sentence cut]
