You should have no problem - the beaches are big enough to accommodate everyone at that time of year. If you walk down to the Tamarells beach bar and beyond they don't tend to be so crowded (and as they are bigger they always somehow look cleaner) - or go right down the Pine Walk towards the Illa d'Or - there aren't the vast expanses of sand, but it's usually possible to find a quiet spot and a bit of privacy. In the past we always avoided the beaches that back on to the road because of the background traffic noise, but this year the new road has taken much of the traffic off the front and it seemed much quieter. We have never felt crowded on a PP beach and we have been at all times of the year (apart from August - but I think even then they are relatively quiet compared to other Mallorcan beaches).