Your question made me chuckle , as I too tend to raise an eyebrow when devices that we now consider to be antiquated continue to be used in research. (When I've conducted sleep actigraphy research, participants were required to wear devices 24/7 that resembled 80s watches!)
And, well, there's good reason for why beepers have persisted: they are cheap enough for you to buy/provide to participants, are effective, they're easier for very young and very old participants to use, and you don't have to worry about inadvertently excluding participants simply because they don't have a smartphone (or other more expensive device--like a tablet) that your methods require.
But yes, there are smartphone apps that have been developed by various entities for ES purposes. I know there's some available on iTunes and Google Play that you can check out to see if they'll suit your needs. Some examples that come to mind include PSYT, iExperience, and PACO.
If you discover something interesting while researching these tools, please let us know!