This is a guide for US listing in passport, as good as any reference for you to use - depends on when and where -there is a summary table in the link that I can’t copy and keep the formatting
Looks like just Jerusalem for the Jerusalem parent, and for the Haifa parent, Palestine if before May 14 1948 and Israel if after.
https://fam.state.gov/FAM/08FAM/08FAM040304.html
8 FAM 403.4-4(A) Israel, the Gaza Strip, the Golan Heights, Jerusalem, and the West Bank
(CT:CITZ-28; 11-06-2019)
a. Golan Heights: Per Presidential Proclamation on March 25, 2019, U.S. policy recognizes the Golan Heights as part of Israel. The POB for applicants born in the Golan Heights is ISRAEL.
b. U.S. policy recognizes that Jerusalem, the West Bank, and the Gaza Strip are territories whose final status must be determined by negotiations.
c. West Bank (including the No Man’s Lands between the West Bank and Israel):
(1) The POB for persons born in the West Bank is WEST BANK.
(2) Persons born before May 14, 1948 in the West Bank may have PALESTINE listed as the POB (if requested).
d. Gaza Strip:
(1) The POB for persons born in the Gaza Strip is GAZA STRIP.
(2) Persons born before May 14, 1948 in the Gaza Strip may have PALESTINE listed as the POB (if requested).
f. Jerusalem:
(1) The POB for persons born in Jerusalem is JERUSALEM;
(2) The POB for persons born before May 14, 1948 within the municipal borders of Jerusalem at that time is JERUSALEM;
(3) The POB for persons born before May 14, 1948 in locations outside Jerusalem’s municipal limits at that time, that are now inside Jerusalem’s declared municipal limits, is listed as PALESTINE or the name of the location (area/city) as it was known prior to expansion of Jerusalem’s municipal limits at any time following May 14, 1948. Persons born in such locations after May 14, 1948, may choose the name of the location (area/city) as it was known prior to the expansion of Jerusalem’s municipal limits; and
(4) Do not list Israel, Jordan, or West Bank for persons born within the current municipal borders of Jerusalem.
g. Israel: List ISRAEL as the place of birth in the passport if and only if the applicant was born in Israel. Do not list Israel for persons born in the Gaza Strip, Jerusalem, the West Bank, or the No Man’s Land between the West Bank and Israel.
h. POB in area formerly known as Palestine: Persons born in the area formerly known as Palestine (which includes the Gaza Strip, Jerusalem, or the West Bank) may object to listing their POB as something other than Palestine. In such cases, you should explain CA’s policy of listing the birthplace as the country having present sovereignty and that U.S. policy recognizes that the final status of the Gaza Strip, Jerusalem, and the West Bank must be determined by negotiations. Applicants may be offered alternate entry place of birth consistent with more specific guidance in this section and in
8 FAM 403.4-5.