At the CMM event Robbie mentions below, Jonathan Tallant discussed a problem for defining presentism. The problem didn't seem to me to problematic, since it assumed the only existential quantifiers the presentism has in her toolbox are one equivalent to 'exists now' and one equivalent to 'existed, exists now, or will exist'. Since this is patently false, that problem seems to vanish.
But there did seem to me to be a problem in the vicinity; namely, that all obvious attemtps at a definition require us to reify times.
Intuitively I can refuse to admit the existence of times and there still be an eternalism/presentism question. Two theorists should be able to have a debate concerning the nature of time and existence without quantifying over times. But I couldn't think how to define the terms without reifying times, and certainly the familiar definitions fail.
Consider 'the only time is the present time'. If there are no times, this is true. So if there can be a presentist/eternalist debate between those who don't reify times, this doesn't capture presentism.
What about 'only present things exist' (where 'exists' here is atemporal)? Nope, that won't do if there are no times. Consider two endurentists who believe that the world started with A, B and C coming into existence. Those three objects proceed to endure through some changes, and then the world ends (taking A, B and C with it of course). So nothing comes into or goes out of existence in this world. At any time it is true that only the things that are present at that time exist atemporally, since A, B and C are the only things that exist at any time, and are the only things that exist atemporally. But that doesn't mean presentism is true at this world: intuitively, there is still a debate to be had between the two endurentists as to whether presentism or eternalism is true.