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I don't know what you mean by "you're not allowed to do a reserved cover."

There is no reason that you shouldn't be allowed to make and accept reserved covers with your Ephemeral horses.

You still need to meet the same requirements as you would with regular horses:
Both mare and stallion must be at least 2.5 years old.
You must have enough energy and time left in the day (25 energy units and 30 minutes, respectively).
The stallion must not be gelded and the mare must not be pregnant or have been covered within the past 10 months.

To cover a mare, you must first offer a covering from an eligible stallion on his personal page. The covering offer must be made specifically to the mare you want to cover, and you must go to her personal page in order to accept the covering.

If for some reason you don't have both a mare and a stallion, you most likely have not finished the tutorial. Go back and finish that tutorial, which will give you a mare and have you "buy" a stallion.