Cisco has support EIGRP as PE CPE routing protocol in MPLS VPN.  It is just like another routing protocol using for PE CPE roituing protocol.  The mechanism is common.  EIGRP in PE talk with EIGRP in CPE to exchange routing, then routing receive from CPE is redistribute to MP BGP (multi protocol BGP) running under address family configuration.  EIGRP receive all VPN routing from reditributing form MP BGP (multi protocol BGP) running under address family configuration.

Configuring RIP for routing protocol between PE and CPE on MPLS VPN cover three steps.
1. Configure RIP on CPE
2. Configure RIP on address-family level on MPLS PE
3. Redistribute RIP to BGP vice versa on MPLS PE