The only thing that can be done is go off season
most of the five star hotels have private beach but then they are expensive eg i stayed lalit goa in sept 2015 and it costed me 5k one day and in general it cost 14 -15k but it was worth or go to secluded beaches like butterfly beach
Best option is to go during the off season - ( Rainy) all the five star hotels with private beaches are very cheap . The rest of the time you can check Holiday Inn amd Radisson Blu . By personal experience they have good quality services and private beach