Euromonitor GMID
Find your country under "Geography". Choose "Category" and find FDI listed under "Economic Indicators". Select over 20 years of time series in five year increments. Includes 5 years of forecasts. Download into spreadsheet format. Very easy to use!

World Development Indicators
Includes 44 years of data back to 1960. Choose your countries, then select the data points. Hint: For FDI, try writing out the terms as "foreign direct investment." Then see the choices for net or gross FDI, in ($) or as a % of GDP.

International Financial Statistics
Choose from tables of available data points by checking the box next to the data that you would like to see. Includes monthly, weekly, or annual data, all from International Monetary Fund sources. Hint: For FDI, look for the categories under "International Fund Position / Direct Investment in Representative Economy".

EIU.com - Economist Intelligence Unit
See the World Investment Service, which is located toward the bottom of the EIU landing page. Choose a country and see the report sections called "Foreign Investment Trends" and "Foreign Investment Data and Forecasts". Search for data or choose a country report. Download data and create charts.