On March 21st of a certain year there was a lunar eclipse what were the coordinates of the moon on that day

I don't know what lunar eclipse you're talking about. NASA's catalog of Lunar Eclipses from 1901 to 2000 does not list any eclipse occurring on March 21st and Wikipedia which covers from 1995 to 2020 does not list any eclipses on that date either. So unless this eclipse occurred centuries ago, you probably have the wrong date.

http://eclipse.gsfc.nasa.gov/LEcat5/LE19…
http://en.wikipedia.org/wiki/Lunar_eclip…

Edit: After further research, I found a March 21st eclipse which occurred in 1810. They don't give RA and DEC, but they do show it's location on a map:

http://eclipse.gsfc.nasa.gov/5MCLEmap/18…

Let's think this through logically.

A lunar eclipse must always happen when there is a full moon.
A full moon must always happen when the moon is exactly on the opposite side of the sky as the sun.
Now I'm assuming we're slightly oversimplifying this question and taking March 21st to mean the Vernal Equinox, which doesn't always occur on March 21st.

If a lunar eclipse happened to coincide with a vernal equinox in the northern hemisphere, that is to say the point where the sun was at R.A. 0h Decl 0 degrees then the moon would have to be at R.A. 12 hrs, 0 degrees.

This is hypothetical though, I tried to find a year where a lunar eclipse fell on March 21st and was unable to find one last century or this century, that is to say I checked from 1900 to 2100 and failed fo find a single occurrence when a lunar eclipse fell on 21st March. If you would like to look for yourself check out www.skyviewcafe.com

Edit to all answers above me:

Everyone is right in their own way:

The first answer is correct in identifying a lunar eclipse in 1810, kudos, I gave up at 1900, after reading your excellent answer I checked the right ascension and declination which coincides exactly with what the third person to answer said. The discrepancy between the answer the third person said and hypothetical answer by the second person is accounted for by the fact that the Vernal Equinox occurred at 06:21 GMT and the lunar eclipse occurred at 02:55 GMT. Answer 2 correctly identified the hypothetical nature of the question but failed to point out that the Vernal Equinox doesn't always fall exactly on 21st March and the moon occupying right ascension 12h and declination 0 degrees during a lunar eclipse is only true at the exact moment of the Vernal Equinox. The third answer is right to point out that on the 1810 eclipse the moon was not at exactly 12h 0 deg but doesn't have any right to crow about it given the failure to recognise the hypothetical nature of the question.