Frances Spiveys' birthday Donna Becks's birthday Sally Barnes's birthday.
The Chicago Manual of Style says:
'The possessive of most singular nouns is formed by adding an apostrophe and an s....' 'The general rule covers most proper nouns, including names ending in s, x, or z....' But, '[t]he possessive is formed without
I should point out that if the surnames are not Spiveys, Becks, and Barnes, but are, rather, Spivey, Beck, and Barne, then you should apostrophize them as follows:
Frances Spivey's birthday Donna Beck's birthday Sally Barne's birthday