If you idea is any good, and the graphic designer has any brains, he should jump at the chance. Which is to say, if you pay equity for something as readily available as graphics designer for a shorter project, then you're way overpaying.
And the irony is, the graphics designer may not be impressed at all, for exactly the reason you give, they often get "work now, maybe we'll pay later" types of proposals.
IMHO you should not do this. Some reasons:
- There are legal fees to consider, you would need to issue new shares or issue a convertible note, and possibly to draft a new shareholders agreement.
- Once the graphics designer gentleman is a shareholder, he may feel inclined to involve himself in business decisions. You don't know if he's good at that part.
How about barter trade instead? I can't speak for your legal situation in your country of residence, but in most places barter trade is perfectly legal, just rarely used. Give him, say, 40 hours of work by you in return for the same from him. Good web designers often need a programmer to customize some CMS/shopping cart/whatever system.
Both parties should agree to providing reasonable estimates for each task up front, and ongoing status information about their progress. Since you're equal partners in this, it shouldn't be hard to reach an understanding on the terms.
NB: The above is assuming that you're talking about a shorter engagement with the graphics designer. If you're considering having him work continuously on your projects without salary, then he's a cofounder and should of course have equity.