For most banks you need a "Cédula de Identidad", but there are some banks and financiaras (very similar to bank and also regulated by the Central Bank of Paraguay) that don´t inittially.
For example Financiera Interfisa where I take most of the Expats I counsel, need some background documentation where they can determine the activities of the Expat, it is better if you can present your Interpol certificate (the one granted in Py) and all other info about you. After you file your request for residency, you should add a copy of the request, in your file at Financiera Interfisa.
Banco Atlas is also another institution where you can open an account without "cédula".
The minimum amount you require for apply for residency, is US$ 5.000,oo
Hope this short summary will be useful.
Kind regards,
Jerónimo