Belinda - I am a little puzzled over some of what you say, nor am I sure what it is you are implying - I wonder if you could help me out?
1. From your OP, you claim that the phrase RIP (Rest in Piece) is mostly/usually used by non-religious people who do not believe in the afterlife - So am I right in thinking that you are implying that atheists using the phrase are hypocritical / possibly offensive?
2.You then support this assertion of yours that this phrase is used mostly be atheists by saying you conducted an in-depth study - in other words, an "argument from authority". Well, if you expect anyone to respect the study you need to link to it, so we can see the raw data and the conclusions you have drawn - the original questions, how the respondents were found/selected, how many respondents, etc. Otherwise, with the greatest respect, it is just anecdote at best, made up nonsense at worst. So, could you either provide a link / reprint the study, or withdraw the assertion?
3.What kind of phrase would you recommend should be used instead of RIP?
More than anything else, I think the phrase represents an expression of comfort to the (presumably) grieving relatives, believer or non- beleiver, and a recognition that, no matter how good or evil that deceased was, most people of good heart try to avoid giving offence - RIP therefore seems a fairly inoffensive term..
To be honest, it all seems a slightly strange to raise a topic on a pretty innocuous phrase..............