The combination of the high guest goal, the wet weather, and the restriction of building only old-fashioned rides make this scenario one of the most difficult Loopy Landscapes scenarios so far. Although you will need to build mostly low-profit indoor rides such as the Haunted House, the Merry-Go-Round, the Crooked House, the Circus, and the 3D Cinema, you can charge as much as $20 for umbrellas most of the time.
You can borrow up to $22,000, so build a roller coaster early on to start bringing in guests and revenue. Do your best to keep most of it underground so that guests will be willing to ride it in the rain. Feel free to build Crazy Rodent-type roller coasters on the surface, but keep their footprints small to keep costs down and save space.
Continue expanding the park as quickly as your budget will allow. Advertise as much as you possibly can to keep your guest count high.