New York Gov. David A. Paterson will propose that private employers be required to offer health insurance to workers' dependents who are ages 19 to 29. The proposal is part of what the administration hopes will be a step toward universal healthcare coverage in New York. Currently, employers are not required to offer health insurance to dependents who are older than 18 or, if they are in college, 22. The proposal expand coverage to some 800,000 people 19 to 29 years old who are uninsured.