How did the final d of "diamond" become voiced in English?

English spelling was irregular and broadly based upon pronunciation until the 1700s when the change towards standardisation started in earnest. The choice, as you see was in the final consonant – French influence and origins favoured the “t”, but English favoured the “d” – and, with waning French influence, that won.

OED

Diamond /ˈdʌɪəmənd/

Etymology: Middle English diamant , -aunt , < Old French diamant (= Provençal diaman , Catalan diamant , Italian diamanto , Old High German demant ), < late Latin diamas , diamant-em (medieval Greek διαμάντε ), an alteration of Latin adamas , -antem , or perhaps of its popular variant adimant-em […], apparently under the influence of the numerous technical words beginning with the prefix “dia”, Greek δια-.

Forms:

α. Middle English diamawnte, dyamawnte, Middle English–1500s dyamaunt, Middle English–1500s dyamant, Middle English–1600s diamant;

β. Middle English dia-, dya-, -maund(e, -mawnde, -mounde, -mownde, Middle English–1500s -mand(e, Middle English dyamonde, dyamount, dyamonthe, deamond(e, Middle English–1500s dyamont(e, diamonde, Middle English–1600s dyamond, 1500s diamont, diamunde, 1500s– diamond; γ. 1600s dimond, 1700s di'mond.