1
general::
Invent, concoct, as in Count on her to dream up some explanation for her absence. This expression replaced the somewhat earlier dream out. [c. 1940]
American Heritage Idioms
2
general::
Phrase(s): dream something up
Fig. to invent something; to fabricate something. (The something can be the word something.) • I don’t know what to do, but I’ll dream something up. • Please dream up a solution for this problem.
McGrawhill's American Idioms And Phrasal Verbs