can you identify what is squeeking? is it the hand-wheel? is it the arm that raises/lowers the needle?
if you can identify where the squeek is coming from someone may have a suggestion---also---what machine it is? brand/model?
you may need to call the customer service 800# and speak to a tech- but having all of the above information handy when you make the call will help the tech figure out the problem-and possibly give you an answer