Hi Paula,
Two Options:
1. With Fiori Client
Yes, X509 with Fiori Client can help you to stop prompting for User Name and password. But, there is a mandatory requirement of MDM Solution for this solution.
SAP supports Afaria with default Fiori Client and if you have a different MDM, you may have to custom build the Fiori Client to support X509 Authentication.
Note: this also requires SAP Mobile Platform.
2. Get the Certificates installed and distributed manually to users and Configure Web-Dispatcher to accept Certificate based login and use Browser on Mobile and Desktop to get this going.
Both the above options needs you to manage the Rule Based Authentication in GW System to validate the Certificates for login purpose.
Regards,
Nagesh