You don't say what board is being used but most Unos, etc., use a ceramic resonator for the system clock, which will typically have a frequency tolerance on the order of ±0.5%. Changing to a crystal (say, ±20ppm) might be simplest, but if you're not in a position to do that, then I'd try a DS1307 RTC. DS1307 breakout boards can be had for under $10, some will plug directly into the headers on an Arduino Uno.
Lately I've been experimenting with running an ATmega328P on the internal oscillator, and connecting a 32.768kHz crystal which acts as a clock source for Timer/Counter2. A simple RTC can then be implemented in software. Fairly straightforward, keeps decent time.