Because the Census Bureau does not collect vital statistics, you are unlikely to find birth and death data broken down by Census Tract.
Vital statistics are collected at the state level. To find information on Live Births and General Deaths in your community:
Centers for Disease Control VitalStats
The Centers for Disease Control has data on births, perinatal mortality and population tables. Data is available at the county level.
National Mortality and Morbidity Weekly Report
The data in the weekly MMWR are provisional, based on weekly reports to CDC by state health departments.
Kansas Health Matters Mortaility Data
Scroll down to Mortaility
Missouri Community Health Profiles
You may find information by zip code or by general area. Statistical information is from 2000 or later and each link results in a .pdf file. Community data profiles are available on various subject areas such as cause of death, chronic diseases, unintentional injuries, prenatal and others.
Information on Communicable Diseases must be reported to local health departments. See Kansas City Communicable Diseases page.
For information on Non-Communicable Diseases, you will also want to check the State Health Department's Website, though you will need to look at the areas devoted to specific diseases for State and (sometimes) County data. Since there are no reporting requirements for non-communicable diseases, the data may or may not be available. See especially the following areas:
CDC Asthma Information