Yes you can, they don’t need to have a paypal account. You can send a paypal invoice to any e-mail address and they can choose the ‘pay by credit card’ option as usual. If that doesn’t work, they can send a cheque or bank transfer, but wait for the funds to clear before posting.
Edited: you have to create an invoice in paypal rather than just ‘request payment’, and you may have to upgrade your account to do this, although I’m not too sure. In the past, basic personal accounts didn’t have the invoice facility, it had to be a premium or business account, but that may have changed.