alternative to screenprinting

i have a question. We have a client, who have bigger quantities of cellulose/coton dishcloth to print, what kind of flatbed machine you suggest for this kind of printing as alternative to screen print....

dishclothes is like this in links:

Maria Dahlgren Blue Cellulose Dishcloth -HUS & HEM- Scandinavian Design For The House And Home

Klippan Leksand Pink Cellulose Dishcloth -HUS & HEM- Scandinavian Design For The House And Home


inks must be eco friendly..........thickness of material is about 1,5 - 2 mm.......