Very slow chemical clock reaction
I assume you are aware of the common clock-reactions, such as the iodine clock, etc. By varying concentration of reagents and pH of the solution, you could run several repetitions to generate a trend-line, and from that extrapolate the estimated pH and reagent concentration to provide you with the time delay you are looking for. The iodine clock is a two-step reaction as outlined below:

In the first, slow reaction, iodine is produced:

$$\ce{H2O2 + 2I- + 2H+ -&gt; I2 + 2H2O}$$

In the second, fast reaction, iodine is reconverted to 2 iodide ions by the thiosulfate:

$$\ce{2S2O3^2- + I2 -&gt; S4O6^2- + 2I-}$$

By decreasing pH in reaction 1 and increasing the thiosulfate level in reaction 2, you should be able to lengthen the ‘clock time’. Let me know how things turn out!