Delaware does issue non-resident licenses. They are issued by the Attorney General and they are valid for 30 days. Also, you may ony be issued 3 permits in your lifetime. I'm not sure why such a bizarre provision is on the books; however, there is no need for a non-resident license since they recognize non-resident permits from states like Florida and Maine which both issue through the mail.
Here. The law...
11 Del Code 1441(k)
(k) The Attorney General shall have the discretion to issue, on a limited basis, a temporary license to carry concealed a deadly weapon to any individual who is not a resident of this State and whom the Attorney General determines has a short-term need to carry such a weapon within this State in conjunction with that individual's employment for the protection of person or property. Said temporary license shall automatically expire 30 days from the date of issuance and shall not be subject to renewal, and must be carried at all times while within the State. However, nothing contained herein shall prohibit the issuance of a 2nd or subsequent temporary license. The Attorney General shall have the authority to promulgate and enforce such regulations as may be necessary for the administration of such temporary licenses. No individual shall be issued more than 3 temporary licenses.