What is the maximum duration my parents could stay here in the UK if I sponsored their visit (from India)? I would like for them to stay for at least 3 months. Is that possible?
As visitors, your parents would normally be allowed to stay for up to 6 months, although there's always the possibility that they'd be admitted for less time.
From the "India" tag I'm guessing they're Indian citizens, in which case they'll need Standard Visitor Visas.
The most likely difficulty when applying for the visa is making a convincing case that they're not going to stay in the UK indefinitely. Showing that have ties to their home country (work, relatives, a home) is the best way to do this.
Citizens Advice have a useful page on helping someone apply for a visa to visit you.