Central American and Haitian Parity Act of 1999 - Amends the Nicaraguan Adjustment and Central American Relief Act (Act) to: (1) extend permanent resident status adjustment provisions to qualifying Salvadoran, Guatemalan, Honduran, and Haitian nationals; and (2) extend the application filing deadline.

Permits certain pending applications filed by Salvadoran or Guatemalan nationals under the Act or Haitian nationals under the Haitian Refugee Immigration Fairness Act of 1998 to be converted to an application for status adjustment under the Act.

Amends such Acts to: (1) authorize the Attorney General to waive certain grounds of inadmissibility; and (2) provide for issuance of immigrant visas to certain spouses and children.

Provides for the limited reopening of certain orders of deportation, exclusion, or removal by certain Haitian, Cuban, or Nicaraguan nationals.