Can you specify what kind of data you are looking for?

If monthly data from weather stations can help you, the global CLIMAT data archive compiled by the German Meteorological Service might be useful:

https://www.dwd.de/EN/ourservices/climat/climat.html?nn=519358

It comprises monthly data of nearly 4000 weather stations worldwide.

It depends on type of data. Here are sources for remotely sensed and in-situ data and in different temporal resolution.

Tropical Rainfall Measuring Mission (TRMM)

Global Precipitation Measurement (GPM)

North American Land Data Assimilation System (NLDAS)

Global Historical Climatology Network (GHCN)

Climate Prediction Center (CPC)

African Rainfall Climatology Version 2 (ARC2)

China Meteorological Administration (CMA)

European Climate Assessment & Dataset (ECA&D)

You can download from a number of sites such as

1. CHRS data portal

https://chrsdata.eng.uci.edu/

2. FAO CLIMWAT

https://www.fao.org/land-water/databases-and-software/climwat-for-cropwat/en/

You can download observed rainfall data for USA from the following website:

1. NOAA Weather Station: https://www.ncdc.noaa.gov/cdo-web/datatools/findstation

2. Downscaled 1km Gridded Precipitation Data: https://daymet.ornl.gov/single-pixel/

3. Downscaled 4km Gridded Precipitation Data: https://www.climatologylab.org/gridmet.html

I usually go to Google and search for weather data for the location of interest. I can usually find the monthly values for max and min temperatures, precipitation depth, and number of wet days. I then enter that information into our online weather generator (https://forest.Moscow fst.wsu.edu) and generate a hundred years or so of daily stochastic climate to drive our erosion models. For example, here is the information for Cairo: https://www.holiday-weather.com/cairo/averages/. I can send you more information on this method if you are interested.