The IFC (a member organization of the World Bank Group) compiled private investment rates over GDP for 63 developing countries during the period 1970-2000.
The data is available in Table C1 of Everhart and Sumlinski (2001) (IFC Discussion Paper no.44).
The data reliability seems to be an issue. Private investment is calculated by subtracting public investment from total investment. The data on public investment, however, may not be accurate.
Stasavage (2002) uses the earlier version of this dataset.