I'm having a bit of trouble with teaching a particular student chords and mastery of those chords. They are just the basic open chords such as C,B,A,G, etc and some dom. 7th chords as well.

Does anyone have any techniques which helped their students learn or themselves really master these basic chords quickly?

I too, would like to know what anyone has to say on this.

Beginner students can have all kinds of problems when it comes to learning chords. Here's a few issues and how I resolve them.
First, sometimes they can't get the chord clean (ie lots of muted strings). I ask them to play the chord as an arpeggio and identify what the problem is. It might be that one of their fingers is fretting a correct note, but is bent in a way that mutes the string under it (or in some cases, muting the string above it). Now they can see that they need to slightly adjust the angle of the finger so that it doesn't touch the string.

Another problem is simply getting their fingers to do what they want. They might play the chord correctly once, but have trouble playing this chord correctly. What you need to explain to them is that when practicing the chord, they need to practicing putting their fingers done in the same order EVERY TIME.
It doesn't help if they finger a D chord by placing 1st, 3rd then 2nd fingers down once, but then do 3rd, 1st and 2nd the next time. They must consistently finger the chord the same way so they develop the muscle memory they need. Finger chords in multiple ways slows down their progress.

Another problem is chord changes. I get my students to do easy chord changes first, that have common fingers so there isn't too much work to do.
Try Em to G (make sure they use fingers 1 and 2 for Em, not 2 and 3), Am to C or D to A. If they are confident in playing the chord by itself, then they need to practice chord changes to a metronome or a drum beat. A lot of students play the first chord, but then take AGES before going to the next one. This is because they are perfectionists and have to make sure everything is right before going to the next chord. A metronome will force them to do it quickly (even if you just put the metronome on 40bpm you should be fine) and they will get the hang of trying to play in time.