Binary stars are usually in stable orbits due to energy conservation: since they do not lose energy, they stay in the same orbit. What can happen over their lifespan is that one of them becomes a red giant and the extended atmosphere transfers mass to the other, changing their orbits, or (more importantly for this question) that tidal forces and gas drag in the envelope causes them to spiral in. Over very long timescales they may also lose energy due to gravitational radiation. However, these are slow processes. There is a lot of energy and angular momentum to somehow get rid of.
For a semi-major axis $a$ the energy is $$E=-\frac{GM_1M_2}{2a}.$$ Interlopers with energy comparable to this could disrupt the system, but the question is instead about causing a merger.
To get a merger the closest distance has to be within $r_{min}=R_1+R_2$ where $R$ is the stellar radius. $r_{min}=(1-e)a$, where $e$ is the eccentricity, which needs to be driven up near 1 so $e> 1 - (R_1+R_2)/a$. For $a=$ 1 AU and $R_1=R_2=$ 1 solar radius, $e>0.9907$ is required.
The eccentricity is $e=\sqrt{1+2\epsilon h^2/\mu^2}$ where $\epsilon$ is the total energy divided by the reduced mass $M_1M_2/(M_1+M_2)$, $h$ the angular momentum divided by the reduced mass, and $\mu=G(M_1+M_2)$. If we want to boost it to a high eccentricity we need to change things so $1+2(\epsilon+\Delta \epsilon)(h+\Delta h)^2/\mu^2 = e^2$.
If we start with $e=0$ we have $1 +2\epsilon h^2/\mu^2=0$, or $\mu^2/2=-\epsilon h^2$ (remember that the energy is negative for bound orbits). So to first order, $2\Delta \epsilon (h^2 + 2h \Delta h) \approx e^2 \mu^2$ or for $e\approx 1$ $\Delta \epsilon \approx \mu^2/h^2$ if we ignore the change in angular momentum (we set $\Delta h=0$). This is essentially a change on the order of $E$.
So if you want a rogue planet to hit and cause a merger, it needs to have about as much kinetic energy as one of the stars - not an easy task, since even Jupiter is 1/1000 of a solar mass, so it would need to move at about 200 km/s to equal the kinetic energy of a solar mass star in a 1 AU orbit.
Were it to happen the time until the merger would be the free-fall timescale $$\tau = \frac{\pi a^{3/2}}{\sqrt{2G(M_1+M_2)}},$$ which in this case is 0.25 year, or about 91 days.
