ACR ACFT REQUESTED HIGHER ALT DUE TO TURB IS ISSUED CLB BASED ON BEING LEVEL IN 2 TO 3 MINS. PLT DOESN'T MAKE ALT RESULTING IN LTSS WITH ANOTHER ACFT.

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ACR X WAS GETTING CHOP AT FL330 AND REQUESTED FL370. PLT WAS ASKED HOW LONG IT WOULD TAKE HIM TO BE LEVEL FL370. PLT RESPONDED BY SAYING 2 AND A HALF TO 3 MINS; THEN CORRECTED HIMSELF AND SAID 2 MINS. I RAN OUT MY 4 MIN VECTOR LINES AND SHOWED I HAD 8-10 MI BTWN THE TIPS OF MY VECTOR LINES. FEELING THAT THE 2 ACFT WOULD BE SEPARATED IN PLENTY OF TIME I CLBED ACR X TO FL370 AND ASKED HIM TO GIVE ME HIS BEST RATE OF CLB. CONFLICT ALERT WAS ACTIVATED AND I RAN OUT MY 2 MIN VECTOR LINES. STILL SHOWING 6-8 MI BTWN THE TIPS I ASKED THE PLT IF HE COULD BE LEVEL IN 1 AND A HALF MINS. PLT ACKNOWLEDGED WITH A 'NO PROB.' ADVISED PLT TO RPT LEVEL IN 1 MIN. PLT SAID 'ROGER WE'RE OUT OF FL360 NOW.' I PROCEEDED TO TURN BOTH ACFT 20 DEGS R. I ASKED ACR X TO RPT LEVEL NOW. HE CAME BACK WITH; 'WE'RE OUT OF FL360 AND A HALF NOW.' ASKED PLT TO RPT LEVEL. PLT ADVISED 'WE'RE AT FL367.' PLT THEN RPTED LEVEL. IT TOOK PLT FROM TIME HE ACKNOWLEDGED THE CLRNC 4 MIN AND 25 SECONDS TO LEVEL OFF AT FL370 AFTER STATING IT WOULD ONLY TAKE HIM 2 MINS. I FULLY BELIEVED THE PLT WOULD BE ABLE TO HAVE HIS ACFT LEVEL IN TIME HE STATED. MY JUDGEMENT WAS OFF BY QUITE A BIT. I WAS TRYING TO HELP THE PLT GET TO SMOOTH AIR AS QUICKLY AS POSSIBLE AND AGAIN; THE PLT LED ME TO BELIEVE HIS ACFT WAS CAPABLE OF SOMETHING IT OBVIOUSLY WAS NOT. I SHOULD HAVE ADDED A RESTR TO THE CLB CLRNC.