I haven't seen a single IC which includes both the necessary gain
stage and the RIAA equalization. They may exist, of course (or could
be made from a programmable-analog part) but I haven't seen them in use.
The commonest approach seems to be to use a dual op amp per channel,
with the RIAA equalization curve being implemented via components in
one or both of the op amp feedback loops. The page at
http://sound.westhost.com/project06.htm shows one such design.
You might be able to do it with just one dual op amp (one stage per
channel).
There are many high-quality audio op amps (low noise, adequate drive
capacity and gain/bandwidth product) which can be used for this sort
of design.