These international organizations now coordinate in producing infant and child mortality statistics, under the name of The UN Inter-agency Group for Child Mortality Estimation (IGME). See
UNICEF, WHO, The World Bank and UN Population Division, "Levels and Trends of Child Mortality in 2006: Estimates developed by the Inter-agency Group for Child Mortality Estimation", New York, 2007.Section 2 of this document is also useful to learn how to estimate infant and child mortality rates from each type of data (vital registration, household surveys, etc.). The resulting estimates are available online at childinfo.org for selected years and at CME Info Child Mortality Estimates for all years since 1950.
Abouharb and Kimball (2007) introduce a dataset on annual infant mortality rates in each country for 1816-2002, by filling as many country-year cells as possible with infant mortality data from a variety of sources (I am not sure if this does not sacrifice the comparability across countries and years). The dataset and the codebook are available at www.prio.no/jpr/datasets (look for the last link for 2007 (vol. 44), no. 6). They avoid using the UN Demographic Yearbooks (which actually do provide annual data in its printed version, but not online) as much as possible. They keep the record on which data source is used, for each country-year observation. It turns out that 41 percent of observations after 1950, mainly developing countries, come from US Census Bureau's International Data Base. I am not sure why we should trust US Census Bureau more than the United Nations.
For poor countries, however, these data may be created by the interpolation of very few data points. See Qian (2015: 303-304).