Hi and welcome to the forum.
I don't know if anyone else knows of long term rental for you but it depends what part of the island you are moving to.
I am in the north of the island and 500 euros is the current rental price, although now we are moving into Spring and Summer the rate is likely to rise considerably. April to October is going to be at summer prices I would think.
There are plenty of private rental signs up on apartments but it is a matter of phoning the number on the signs once you get here.
Most of the Spanish people that we know already have their apartments booked for the summer months but hopefully someone else can help.
The free paper over here is Euro Weekly News at
www.euroweeklynews.com which might be worth taking a look to see if you can access their advertisement pages or Mallorca Daily Bulletin
www.majorcadailybulletin.comAlso have you taken a look at
www.kyero.com or
www.thinkspain.com for their rentals?
Good luck with your search.