Billable is all I could come up with..."My lawyer searched for all the billable hours he could come up with."
Unless you could do something with "unfillable" or "fillable" as in "The prescription was unfillable." Ditto: unkillable ("The superhero was unkillable.") and so forth.
Rhyme zone and Rhymer.com provide many verbs with -ill endings that you can try this pattern with.
You could also try doing something silly, like "ask her if she will nibble something..."
Okay, well, you can't say I didn't try! 8)