Word for word that comes out to "Er könnte es getan/gemacht haben", (not sure if they prefer tun or machen here) but that really doesn't make any sense in German.
They would say "Er hätte es tun/machen können" which really doesn't make any sense in English.
"hätte" = "would have"
"tun/machen" = "do/make"
"können" = "(to) be able to"
That comes out to something like "He would have be able (to) make it". Switch "be able to" to past tense "been able to" and it's functional English. I've no clue why they use present tense here, but I'm not German. 'Just go with it' is often the easiest approach.
"Konnte" is past tense ("Yesterday, he could do it, but today he can't"), and "könnte" is subjunctive ("He could do it if he had time"), and both of them translate to "could." You ought to be able to put in either one, though as a stand-alone sentence I would tend to favor the subjunctive "könnte." (For past tense, I would usually say "could have done it" in this particular sentence.) But if "konnte" isn't working, I'd say it certainly should.