Most women simply did not wear earrings during the regency period. This was a period of quiet natural elegance, where the woman's toned body and pure skin were on display. If anything, it was the beautiful hairstyles which adorned the head, with ribbons, pearls, tiaras and other items decorating them. The ears were simply a part of the face which sat beneath the hair.
Regency Period and Jane Austen
However, sometimes women did decide to wear earrings. When they did, the earrings were small, tasteful, and on wire. They did not wear posts in the regency era.
Here is Charlotte from the A&E version of Pride & Prejudice. Remember that Charlotte was the most well to do in her neighborhood, and her mother tried to dress her "fancily" in order to get her a husband. So this might explain why she had earrings and the others did not.
In another image, Mrs. Clay in Persuasion from Masterpiece Theater is wearing a simple pearl design.
Note when you search on the web that there was a COMPANY named Regency that made big, gawdy rhinestone designs in the 1950s. This is NOT REGENCY ERA JEWELRY :)
Regency Rings - simple in design
Regency Necklaces - crosses, pearls
Regency Earrings - wire, not posts
Regency Period Information