The skatepark was given the go-ahead by the tennis club and councillors in April, but since then the club has had a surge of new members sign up and was desperate to save one of its three tennis courts in Sandhurst Memorial Park from development.
Councillors and tennis players came to loggerheads over this issue at a meeting of the leisure committee in July.
The final decision was made at a full council meeting last week when a majority of 10 to six votes against was recorded.
Cllr Paul Bettison, who was in favour of the development on the tennis court, said: "There is not the space to do everything for everyone in the way they would like.
"However, we will help them (the tennis club) in the future, but we have to take decisions about what is here and now and that is there are children skate boarding on the pavements and they're a danger to themselves and us.
"I would not like it on my conscience if there was an accident."
Cllr Diana Pigeon, who was against plans for a skatepark being built on the tennis court, said: "We have always supported the football club and now tennis has developed into a club and needs to have three courts in order to compete in the league.
"There are no other sports facilities for ladies, and we would be saying good bye to another club if we put the skatepark on the court."