Avoid if possible; the phrase “[x] was caught lying and sheepishly acknowledged it” is preferable.
One afternoon he noticed me sheepishly looking at the screen.
When asked shortly after sitting down about his (now slightly faded) purple hair, he sheepishly replied, “My mom does it.”
She complied, albeit sheepishly, mouthing one that was surprisingly conventional and all-American.
If you ask for it sheepishly, you might as well not ask at all.
"I never saw him so bad before," said the other, sheepishly.
"We were going to hunt up a parson in Upper Chester," said the Captain, sheepishly.
"Yes; I have a sort of recollection of it," answered Nugget sheepishly.
"You're right—and wrong, Phil," Cloud stated, not at all sheepishly.
sheepishly, but still trying to look as though he didn't care, Cheapside hopped out into the passage and Dab-Dab closed the door.