B24 STUDENT PLT AND INSTRUCTOR PLT HAVE AN NMAC WITH ANOTHER ACFT IN THE PATTERN AT A TWRED ARPT.

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I WAS GIVING INSTRUCTION TO A STUDENT. HE WAS IN THE PATTERN (L TFC FOR RWY 4). I HEARD A DIAMOND ECLIPSE CALL TO THE TWR THAT HE WAS INBOUND FOR LNDG FROM THE SW. THE CTLR CLRED HIM TO LAND FROM A DISTANCE OUT. AS MY STUDENT REACHED MIDFIELD; HE CONTACTED TWR AND WAS SUBSEQUENTLY CLRED TO LAND WITH NO RESTR. UPON REDUCING PWR ABEAM THE NUMBERS; I NOTICED THE DIAMOND STILL INBOUND ON FINAL; SO I ADVISED MY STUDENT TO LET THE DIAMOND PASS BEHIND US BEFORE TURNING BASE. AT THIS TIME; THE PIPER ARCHER; WHO WAS IN THE PATTERN BEHIND US CALLED FROM MIDFIELD AND REQUESTED A TOUCH AND GO AND WAS CLRED FOR '#2 CLRED TOUCH AND GO' AS SAID BY THE CTLR. AT THIS TIME; THE ECLIPSE WAS ON SHORT FINAL AND WE WERE TURNING AN EXTENDED FINAL. I STARTED LOOKING FOR THE ARCHER AND COULD NOT LOCATE IT WHILE INBOUND ON FINAL. AS WE CLOSED IN ON SHORT FINAL; THE CTLR ASKED THE ARCHER IF HE HAD THE TFC IN FRONT OF HIM IN SIGHT AND AS HE WAS SAYING THAT; THE ARCHER FLEW RIGHT OVER OUR HEADS; DSNDING ALMOST ON TOP OF US. THE CTLR TOLD THE ARCHER TO FLY A R 360 DEGS FOR SPACING AND CLRED THE PLANE AWAY FROM US. IT WAS ALMOST A VERY BAD SIT. ALTHOUGH I KNEW WHAT THE CTLR HAD MEANT WHEN HE GAVE US CLRNC TO LAND; THE OTHER PLT WASN'T AWARE OF THE ECLIPSE COMING IN AND MIGHT HAVE MISTOOK THE ECLIPSE FOR US. BETTER COM AND LISTENING TO WHAT WAS GOING ON WOULD HAVE PREVENTED THIS SIT FROM GETTING THIS FAR.