Steve loves to play the piano but doesn't like practicing the exercises his piano teacher assigns. Steve knows the exercises will help him play better though, so he tries to motivate himself using his favorite treat—chocolate chip cookies.

To find the constant of proportionality in the relationship between the time Steve practices the piano (x) and the cookies he gives himself (y), we can use the formula for proportionality:

\[ k = \frac{y}{x} \]

We'll calculate the constant of proportionality using the given pairs of values:

1. For \( x = 2 \) and \( y = 4 \): \[ k = \frac{4}{2} = 2 \]

2. For \( x = 3 \) and \( y = 6 \): \[ k = \frac{6}{3} = 2 \]

3. For \( x = 4 \) and \( y = 8 \): \[ k = \frac{8}{4} = 2 \]

4. For \( x = 5 \) and \( y = 10 \): \[ k = \frac{10}{5} = 2 \]

In every case, the constant of proportionality \( k \) is 2.

Therefore, the constant of proportionality is \( \boxed{2} \).