Having a quick look at the Gloucestershire Genealogical Database

from 1500 to 1600

Seaching by CONSTANCE

WILLS

1544 COWSTANS - Roger (Westbury on Severn)
1570 CONSTANCE - Thomas (Westbury on Severn) Husbandman
1576 COWSTANCE - Philip (Stanway) - Labourer
1589 COSTANCE - Richard (Flaxley) - Butcher
1591 CONSTNS - John (Westbury on Severn) Weaver

Will have a look at these Wills which should be on Ancestry (could be in Latin/early English - difficult sometimes to read!!

Transcriptions on the Forest of Dean Records

Flaxley - baptisms

Anne CONSTANS - 1567
Robert CONSTANS - 1567

Use the Soundex on the Record Search (quite a few COWSTAN/COWSTANCE or even COUSTANS/CUSTANES etc)

See later reply: i.e baptism 1726 of Elizabeth CONSTANT alias COWSTANT at Newent