While pictures would certainly help, I think we can narrow down the search a little bit, based on the given information.
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The copper coin was found in a roman sector in a desert in northern Egypt.
Under early Roman rule, Egypt was the personal property of the Emperor, who maintained a closed economy there - normal Roman coins were invalid in Egypt; special provincial coins were struck for use there, which were invalid in the rest of the Empire. So your coin is most likely a Roman Provincial. Any writing on it will be in Greek, rather than Latin.
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There is a left facing head with a beard and a wreath on his head.
Beards were only fashionable on Imperial portraits for a relatively brief window, roughly 100 to 300 AD, and most of the bronze coins from 200-300 AD depict the emperor wearing a spiky crown, rather than a laurel wreath. So it's most likely your coin comes from the second century AD.
Left-facing portraits are also rather unusual during this period; the usual convention at this time was to face right.
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On the reverse, a woman is lying on a couch.
You're sure it's a woman? Though reclining females are not unknown (
here is a rather worn Hadrian drachm with a reclining Tyche), a much more common depiction on Romano-Egyptian coinage was the reclining river-god Nilus, who was male.
This example, another drachm of Hadrian, is typical.
If you can tell us the size, that could also narrow down the search. Meanwhile, have a scroll through the
Wildwinds page for Roman Egypt, particularly focusing on emperors from Hadrian to Severus Alexander. Use your browser's search function on that page to find "seated" or "reclining" types, and see if you can see a match.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis