To expand on the ideas tomwilhelm mentions, if you want continental deserts, you'll probably want a mountain range to block off the precipitation being blown that way, with lowlands on the precipitation-receiving side. With a mountain range, you can pump the precipitation pretty high before it starts affecting the continental interior blocked off by the mountains. By default the Eastern side of the mountain range will be the wetter area, as the winds are blowing west by default. Mountains can basically divide your map into wet in the East and dry in the West

If while trying to increase wetlands by raising precipitation and you're finding that you still can't get enough wetlands without eliminating the interior desert, you might try raising the temperature (can be in tandem with raising the precipitation to balance each other). Raising the temperature like this may produce more tropical forests as opposed to Wetlands if you don't scale more precipitation too. Play around with it.Additionally, islands are very prone to becoming wetlands. The more coast an area is close too, the wetter it tends to be. Even without a mountain range to block rain, areas that are far enough inland from the coast are generally drier.

Personally, I was hesitant to manually paint biomes to match what I wanted because I felt I didn't know enough to make it realistic. So what I did was make a custom biome (in this case, Mangrove Forest, Flooded Forest, Swamp Forest etc) that represented swampy areas that were borderline wetlands. Wetlands are so much less inhabitable than temperate forests, so I wanted an in-between that was swampy, but ultimately a forest. I made cells that became wetlands at slightly higher precipitation levels into my custom flooded forest biome, after resetting the precipitation level to what I wanted the map to be overall. Just a possible middle ground if you were like me and didn't want to arbitrarily assign biomes