MATLAB fvtool: Setting the passband ripple below 0dB for a FIR Filter
From your question I conclude that it is an equi-ripple filter that you designed, probably using the Parks-McClellan algorithm. Such an equi-ripple FIR filter has a magnitude response alternating between the values $1+\delta_p$ and $1-\delta_p$ in the pass band (where $\delta_p$ is the maximum approximation error in the pass band), and in the stop band it also has ripples of equal height $\delta_s$, where $\delta_s$ is the maximum stop band error. Note that all quantities I use here are linear, not in dB.

So, as mentioned by SleuthEye in a comment, after designing such a filter you can simply scale it to get the desired behavior. If $h[n]$ are your original filter coefficients, your desired filter has the coefficients

$$\tilde{h}[n]=\frac{1}{1+\delta_p}h[n]\tag{1}$$

The filter in $(1)$ will have a pass band magnitude alternating between the values $1$ (i.e., 0 dB) and $(1-\delta_p)/(1+\delta_p)$, and its minimum stopband attenuation will be $\delta_s/(1+\delta_p)$.