Where can I find disease diagnosis datasets?
CDC Wonder, a health database of the US Center of Disease Control and Prevention (CDC), has weekly data for Nationally Notifiable Infectious Diseases and Conditions, United States: Weekly Tables from 1996 to 2020 on the state level for antrax, brucellosis, dengue fever, leptospirosis, malaria, meningococcal disease, Q fever, rabies, etc.

Weekly tables since 2014 are available on Data.CDC.gov.

Weekly tables for 1952-2017 published in the MMWR are available at CDC Stacks MMWR and weekly tables starting in 2018 are available at CDC Stacks NNDSS.

HealthData.gov has two weekly datasets for malaria by US states - here is one.

Open Government Data (OGD) Platform India has data on a district or state level, for example, for malaria.

Keywords that can help in further search:


infectious disease
week or weekly report or data 
MMWR (Morbidity and Mortality Weekly Report)
surveillance


Keywords, like diagnosis or outbreak, can limit your search too much.