Multiple entry Indian visa for American citizen kids , Reentry

[majety]

My two teenage kids are in India for 5 months. They were in high and middle schools in US in the beginning of the academic year and took permission to do their syllabus in India as online students of their respective schools. Now they are about to be admitted in Indian boarding schools in India. Their current visa is valid for 6 months which is fast approaching deadline now. Can I take them out of the country to a neighboring country and come back so they have six more months of tourist visa? I will apply for student visas once their admissions are completed in June. But for now to be legal they need to have more visa time on their passports. Which country is the easiest to go to and come back , probably on the same day?

Thanks very much in advance for guidance.