There are three things you need to make sure:
1) Check that the employee’s child details are correctly entered in the eLeave > Leave Admin > Child Details (Note that for Singaporean child, you need to tick the ‘Pro-family leave’ option in order for the employees to be entitled to childcare leave for Singaporeans.)
2) Check that in your Leave Setup > Company Setup page, that under 'Child Care & Extended Maternity Leave Setup', the options for the leave types are enabled.
3) Check under Leave Setup > Leave Types, that for the different types of childcare leaves, the leave types are not restricted to a specific gender. If an employee does not fulfill any requirements of the leave type, he or she will not be able to view the leave type from the dropdown list. For example: if the 'married' option is checked in the settings, and in the eLeave > Set Entitlement page the 'married' option is not checked for the affected employee, he/she will not be able to view the leave type.
After those configurations are done, your employee should be able to view the leave type in the leave application page.