Delay-tolerant networks (DTNs) are an emergent communication paradigm characterized by intermittent connectivity. The nodes in DTNs can take advantage of their contact opportunities to forward messages. However, in noncooperative DTNs, the nodes may be selfish and reluctant to cooperate with each other in message forwarding. In such DTNs, stimulating cooperation among the nodes will be indispensable. Recently, many incentive mechanisms have been proposed to motivate nodes to cooperate in message forwarding. However, most of them cannot guarantee systematic security. To resolve the drawback of the previous incentive mechanisms, we first propose a credit-based rewarding scheme called the earliest path singular rewarding (EPSR) scheme to motivate the nodes to truthfully forward the messages during every contact opportunity. Then, we propose another credit-based rewarding scheme called the earliest path cumulative rewarding (EPCR) scheme by further considering that a node may get more contact information on others. We prove that both the EPSR and EPCR schemes are incentive compatible, and the payment for each delivered message is upper bounded. Furthermore, the proposed schemes can prevent selfish nodes having malicious behaviors. We have conducted real-trace-based simulations to illustrate the effectiveness of the proposed EPSR and EPCR schemes.