The tennis club near Marineland is called Sporting Tennis and it has 7 or 8 courts. I am playing there this morning. They may have members but I don't know any. This is probably the most "turn up and play" of the clubs, however there are many and all allow none members. Courts range from 12 to 15 euros. There is quite a large municipal centre in Magaluf - on the same road as Goodfellowa but about 600 metres further inland. The courts are all first class.
On dress code Mallorca is very relaxed. The only very strictly enforced code regards shoes. As most of the courts are clay deeply treaded training shoes are very frowned upon simply because they cut up the courts badly. Clay court tennis shoes have very amny small ridges and grooves to give grip when required, allowing sliding and not damage the surface. Old fashioned pumps are great - you are supposed to slide on clay!!
You can almost always get courts in high season at "mad dogs and englishmen" times of day!! i.e. the locals don't tend to play much from 11.00 am until 4.00 pm - it's too hot. The odd hour during that period can be great fun though.
Tennis is generally great here for people of all ages and abilities. If you need coaches they typically add about 25 euros per hour to the cost of the court and whilst my coach is due to have her baby in May, I would be happy to put you in touch with others that we've used in the past if you want.