I can think of a few reasons Constantine II's coins as
Augustus may be, or might appear to be,
scarce.
1) We are only talking about a short period of time - from becoming
Augustus in 337 to being killed in 340: 2-3 years.
2)
Constantine II himself only controlled three mints: Trier,
Lyon and
Arles. One might expect that
his brothers (
Constans - who he died fighting, and
Constantius II), who controlled the other mints, issued less coins for him than for themselves.
3) There was only a single common
type issued by
Constantine II for himself during the 337-340 time period:
Gloria Exercitvs with one
standard, a
type which
had also been issued under Constantine from 335-337. Given that
Constantine II shared
his fathers name (no more
IVN or
CAES to distinguish them after he became
Augustus), and even adopted
his MAX(imus) title, it's common to see coins of
his misattributed to
Constantine I.
4)
Constantine II was also issuing other
types which should be added to the total:
Vrbs Roma,
Constantinopolis,
posthumous Constantine
quadriga,
posthumous Helena Pax Pvblica (not a
complete list, but the commoner ones).
Finally, if you look at the Helvetica spreadsheet (which doesn't differentiate between the 335-337 period under
Constantine I, or 337-340 under
Constantine II) for the
Gloria Exercitus one
standard type, at Constantine II's Trier,
Lyon and
Arles mints, you can see that it's even scarcer for
Constantine I than
Constantine II, so maybe the output of these mints simply wasn't that great at that time. The
type was commoner at Constantius II's mints (
Siscia,
Thessalonica,
Heraclea,
Constantinople,
Nicomedia,
Cyzicus,
Antioch,
Alexandria), and it might be instructive to compare the marketplace
rarity of the
type at those mints for
Constantius II vs
Constantine II as
Augustus. Conveniently the
type ended in 340, so you don't need to look for anything to identify the time period other than title of
Augustus (although you would need to differentiate CI from CII).
Ben