It seems that there was a trend to gigantism in ornithopoda,
ceratosauria, pachycephalosauria, sauropoda, coelurosauria and
crocodylia.
I'm not a huge fan of "Cope's rule" - in general, and especially when
applied to dinosaurs. Take sauropods for example, the biggest of 'em all.
There was certainly a rapid shift toward gigantism in the early history of
sauropods (Late Triassic/Early Jurassic). But in terms of overall body
mass, sauropods appear to have peaked in the mid-Mesozoic (e.g.,
_Brachiosaurus_ and _Seismosaurus_ in the Late Jurassic, _Argentinosaurus_
and _Sauroposeidon_ in the Early Cretaceous). But in the Late Cretaceous,
the sauropods appear to have gotten smaller overall. By this time, the vast
majority of sauropods were titanosaurians, and most of these tended to be on
the smaller side - especially the saltasaurines. Somebody actually did a
study on this - Barrett and Upchurch (2005), I think it was.
For every extinct lineage that got bigger over time, there's probably one
that got smaller, and one where the taxa stayed around the same size.
Ornithopods and ceratopsians certainly appear to have gotten bigger
(courtesy of hadrosaurs and ceratopsids, respectively), but alvarezsaurs and
stegosaurs seem to have gotten smaller. (Also keep in mind that sample size
may make any such perceived 'trends' statistically meaningless.) I know
there was a study by Hone et al. (2005) which claimed to show that most
dinosaurian lineages got larger over time. But if you dig a little deeper,
the evidence is actually rather weak. The same is true of most of the
attempts to demonstrate Cope's rule in other lineages, with horses being the
most (in)famous example. Stephen Jay Gould called Cope's rule a
"psychological artifact".