Tim,
LDS(Mormons): http://www.familysearch.org/Eng/Library/FHLC/frameset_fhlc.a... have the older Vital records on microfilm, and can be searched in your nearest FHLC(Family History Library Center), for the Film numbers follow the links after Place search until you see View film numbers in the upper right corner:

Roman Catholic parish register of births, marriages and deaths for Bodókőváralja, also called Boldogkőváralja.

Greek Catholic Church register of births, marriages and deaths for Bodókőváralja, later called Boldogkőváralja.

Civil registration of births, marriages, and deaths for Bodókőváralja, Abauj-Torna, Hungary. Text in Hungarian. Civil registration began October 1895.

MATAV Hungarian phone directory doesn't have Király listing in Boldogkõváralja, the closest one is in the neaby Abaújkér:

Király Antónia, Király József and Király Józsefné (Mrs.József Király) 3882 Abaújkér, Rákóczi út 62/a
(47) 332-029

You could write to the Mayor's office:

BOLDOGKŐVÁRALJA KÖZSÉG ÖNKORMÁNYZATA
Polgármester(Mayor): KÓCZIÁN GYULA
3885 BOLDOGKŐVÁRALJA
Petőfi utca 28.
HUNGARY-EUROPE

Jegyző neve (Town clerk): Budai Emilia
Lakosságszám (Population): 1094
Körjegyzőség székhelye (Jurisdiction center): Boldogkőváralja
Megye (County): Borsod-Abaúj-ZemplénTelephon/Fax: 46/387-703

Abaújkér City hall has Email address: abaujker.onkori@econet.hu