90 Day notice period! How to get away?

I have been searching for jobs since last few months and initially I used to mention my notice period as 90 days. Recruiters used to treat me like minorities in this country. Then I updated it to 60 days actual still being 90 days. However, I started fetching interview calls and eventually cracked one today. The company wants me to join ASAP with an option to buyout the notice period. However, my current company is stuck to age old 90 day notice period and I don't think there's a buyout option with them. I do have seen a case of 37 day release but need help in ways of tackling with this 90 day NP. P.S. Deployed on client side. Have amazing working relationship with the client manager. But don't want to utilise that as I am not sure if it will turn out good or bad. As I have seen things turning hostile once you put down papers. Any suggestions would be really helpful! Thanks.