Click on Right Pedal Downstroke
 

And it's gotten worse. I checked the mounting screws for the crank and the nuts into the bottom bracket. The pedal crank doesn't seem to be hitting anything. When you pedal lightly or pedal with your hands, there's no noise. It's only on the right pedal down pedal not the left. Thank you.

Do the nuts for the bottom bracket have to be tightened against each other? Instead of one at a time.

Bottom bracket noises are a pain to diagnose because the range of possibilities is so great.

You say you checked the spindle bolts, so I'll assume you have a square taper crankset. So no, you don't tighten the spindle bolts against each other. Each is independent and tightened while holding the cranks from turning.

Since it's only the right crank that clicks, start with the most basic, which is also the easiest to diagnose. Remove the right pedal, clean and grease the threads and mating surfaces then remount the pedal fresh. About one third of the time this will cure the problem, but if not, try again using a different pedal.

If it still clicks with a substitute pedal, come back, and you'll get a long list of next steps from myself and others. (for your sale I hope it's the pedal)

Unless you clearly hear the noise from the right crank area don't count on it being the right side. Sometimes the release of pressure on the left crank can cause a click. Do both pedals and ideally try a different pair if the click persists. You said you "checked" the screws/nuts (actually either a bolt or nut) but does that mean you saw they were not loose or that you tightened them? Another common cause on the right is the chainwheel bolts.

This ia a Schwinn 754 aluminum, maybe mid 80's. I checked the crank mounting screws and they were tight. Haven't had a chance to remove and check the pedals. Thanks everybody.

Checked the pedal, my hex key didn't fit. But guess what? When I took off it was quiet. It sounded beautiful. For a while. Will check again when I get correct allen wrench.

Make sure the crank arm isn't hitting the front derailleur cable.

It is funny (funny-strange, not funny-ha ha) but I have 4 bikes that I rotate thru regularly, and I think 3 of them had this same symptom: they had an audible click when the right pedal was at about 1 o'clock on the downstroke. All aluminum frames; some outside bearing BB's, one Octalink.
I have started disassembling the BB's, cleaning then reassembling using teflon tape on the BB cups and pedal threads.
So far, so good. All has been quiet since maintenance.
I had always checked tightness of cranksets, chainring fixing bolts, BB torque, lubed pedal threads, tightened handlebars and stems.
I have even replaced my pedal cleats and tried different shoes. Nothing solved the problem till the teflon tape.