Firstly, a rant. I deplore and detest the word notifications. It should have no plural. It is designed to be an uncountable noun and, therefore, not capable of pluralisation. It derives from the verb notify so it focuses on the act or fact of giving or receiving notice.
Facebook and the rest make me foam at the mouth with the revolting 'You have received new notifications'. No, my darling, stupid Facebook, you are referring to actual notices so just call them notices. You are not trying to say anything about the act or fact of giving notices, you are communicating something about actual notices - new notices are awaiting attention.
You will find other examples where the long word (often ending -ation) is used when the shorter word is better. An example that springs to mind is motivations - no such word in my book. Motivation is the general idea of having motives, so it already carries a plural sense; if you want to talk about certain movites, then just say motive or motives. This practice is the result of people mistakenly believing that longer words make them seem better educated.
Turning to the matter in hand, I suggest a simpler start with 'We are able to provide notification by telephone and, possibly, e-mail.'
Notification strikes me as right here but notice (again as an uncountable noun), or notices might work well depending on context.
If you want to surround possibly by commas, there is no need for a comma before and. The commas act as weak brackets. Take possibly away and there would be no comma before and, so why insert one just because you add possibly?