Requiescat in pace -- May he rest in peace.
I know of three conventions you could follow. I present them in the order of my preference.
The most classic, formal, and supportable convention is to have the dot after every letter. "R.I.P." That shows that each letter is an abbreviation for something.
A less formal, most modern choice is to ignore the punctuation entirely, except to force upper case. "RIP". This model seems to be related to our recent habit of generating acronyms at the drop of a hat, and typing them quickly with CapsLock firmly depressed.
A purely decorative choice is to use separating marks between the acronym's letters. "R∙I∙P" or "R*I*P" or "R-I-P". That's the sort of stylistic choice that makes people go "eww, what were they thinking?" once it has dropped out of fashion. I consider it a good thing that this has nearly dropped out of fashion.
Even if you do use this last choice, you shouldn't use normal periods for the separating marks. Raised dots are the least bothersome, when available, or hyphens otherwise.