Have you looked at ATT Wireless Go Phones? They have a flip phone for $17.99. Or find a cheap used phone on ebay or somewhere, and just put in their sim card. One of their most basic usage plans costs a flat $2 for each day you actually use the phone no matter how long you talk (add $1 for data). For your described use that might be $4/month for airtime.
My wife and I have been happy with Consumer Cellular. But their lowest cost plan is still $10/month, no minutes included. For us it works; our combined bill for 2 phones is a steady $43/month.
