Portal Carmabola is a great option if you want to experience Iberá at night. If you hire a local guide you can stay in a refuge (per visitor AR$50) built in the style of the local houses on the park grounds. An even better option is to stay with a local family in the community besides the park atop their mound with 360-degree views of the plains.
It's possible to pitch a tent for a small fee in the Portal Carmabola community and order meals from locals.
There was nowhere to pitch a tent within the national park when we visited although there are plans to construct a campsite a short distance from the port.