One of the tipoffs for bad distributor bearings is supposed
to be red dust in the distributor cap. I'd still be amazed
if the bearings had already gone bad again, but I hear you
about the noise sounding the same.

Another possibility:
Do you hear the clicking both when the engine is relatively
cool (after a morning start, for example) and after starting
when it is already warm?

If so, this implies the intake/exhaust valve lash is set a
little high but not necessarily out of spec.

When was the last time the valve lash was adjusted?

You did replace only the housing, right? On a car this old
the shop that replaced it might have figured you needed a
new igniter and coil at this age as well, for an extra $200
on top of the cost of the housing. To a customer not
particularly knowledgeable on the subject, that would be
easy to sell using the line, "You really need a whole new
distributor." Housing, coil, igniter, wha??

An advanced beginner with a decent set of wrenches and
sockets, a bit of patience, and a willingness to follow the
directions closely can definitely replace both of these on
his/her own. Do not overtighten the little distributor cap
bolts. Do not overtighten the bigger distributor housing
hold-down bolts. Both are just snug: Don't he-man them. (I
"He-Manned" the distributor cap bolts once and sheared the
thing off.) Preferably you'll use a torque wrench on the
hold-down bolts.

The first step to take is not in the manual and was a little
confusing to me the first time. Here it is: People in the
honda newsgroups advised marking the distributor and
camshaft housings so one does not have to re-check and
possibly adjust the timing. If you look at the three large
bolts that hold the housing in place, you'll see that the
flange through which they extend allows one to rotate the
whole housing assembly clockwise or counterclockwise. This
adjusts the ignition timing. I did not understand this until
I got the housing loose. Then it's too late. Yet it's  not
catastrophic. Post if this step does not make sense. One can
actually kind of see part of the line I drew with a sharpie
market on my 91 Civic's housing at the bottom of
http://home.earthlink.net/~honda.lioness/id5.html . Look
just to the right of the top distributor housing hold-down
bolt. It's a little to the right of dead center of the
photo.

The second step is the only really tricky part:
Disconnecting the two electrical connectors to the
distributor. Figuring out which tab has to be pressed and
which way etc. always baffles me for 10 minutes or more. Go
slow. Have a tiny screwdriver to insert into the tab area to
mess with it until it comes free. It shouldn't take much
force at all.

Then follow the steps at www.autozone.com 's free online
manual for the 91 Civic. On the left at the autozone site,
click on "Repair Info," then "Vehicle Repair Guides." Click
on car year, make, and model, etc. Or use the steps given at
http://techauto.te.funpic.org/index.php?content=Ignition
(which does talk about making the mark I suggest above, only
using a razor blade).

See the autozone manual for directions for removing the
coil. I think removing the coil first makes removing the
igniter easier.

Here are directions for the igniter, or again see the
Autozone manual's directions.
http://www.marklamond.co.uk/howto/electrical/igniter/igniter
.htm

Tegger's unofficial FAQ site also has a lot of commentary on
both of these. It's worth reading at least once quickly,
taking notes as needed about removal, before you begin. See
http://www.tegger.com/hondafaq/faq.html#startprobtop .
Unfortunately the link for how to replace the igniter isn't
working at the moment. Tegger?

Good luck. Updates are welcome, since they help people in
the future.

Also, I would consider the other suggestions here (e.g.
Burt's re the Tach resistor) as well. Diagnosing over the
internet is hard but not impossible. Hang in there. These
vintage Hondas are amazing in their tenacity.