How can I change the number of times my iphone tries to notify me when I receive an SMS message? I would like to change the number of times my phone 'pings' me when I receive an SMS message. 

I'm not sure who decided that 2 pings was enough and there would be no visual indicators but I would like to at least change the number of times it tries to tell me I got a message.
You can go to Settings > Notifications > Messages and change the Repeat Alert option to Never. This will stop it from bugging you twice!