I am given to understand that there is a slight difference between how 'could' and 'could have' are used to denote past possibility.
How beautifully expressed! and with a Title like A foray into understanding Past Possibility., I hope my response goes some way to easing any hostile tension between you and the tenses.
He could be in a different city on that partcular day.(General past possibility)
NO. Imagine John's secretary in Madras is talking to me about trying to arrange to see John who is busy and just leaving on a trip around India. I say, "Can I catch him in Delhi next Thursday? I'll be there on that." The secretary says: "Next Thursday? I'll check his itinerary. He could be in Agra on that particular day."
The tense indicates future possibility.
He could have been in a different city on that partcular day.(Perhaps he was in a different city)
Yes. This is in the past. We didn't catch up last Thursday. He was supposed to be in Agra on Thursday but maybe plans got changed. "He could have been in a different city last Thursday."
Either of these sentnces denotes past possibility. But I am not what is the real difference between these two sentences.
Are you still in doubt with these two sentences?
Getting jobs could be very easy in the USA in the 1950s. (General possibility)
'could be' indicates something in the future: "He could be an astronaut when he grows up."
He could have got the job easily with his formidible (note the correct spelling) qualification.(Perhaps, he got the job easily)
NO. He didn't get the job. "He could have got the job easily with his formidable qualifications, but he comes across as so arrogant and full of himself employers don't want a bar of him." OR "...if he had applied."
Note: 'formidable' is pronounced as in "FOR-midable'. Not that ear-jangling oh so frequently heard 'forMIDable'