Leading-order cause of diurnal (not semidiurnal) variations in $g$? The following graph shows the result of a very impressive differential measurement of the gravitational field in Boulder, Colorado, over a period of a couple of days.

Floris got it from a description in a book and posted it as part of an answer to this question. Based on the caption, I'm guessing that the experiment was described in this paper by Zumberge, which I don't have access to.
There is excellent agreement between theory and experiment, and the main features of the graph are these two Fourier components:


*

*period=12 hrs, peak-to-peak amplitude $\approx 1.8\times10^{-7}g$

*period=24 hrs, peak-to-peak amplitude $\approx 1\times10^{-7}g$
In addition, there is a slower trend, which I assume comes from interference between the solar and lunar effects.
Assuming a perfectly rigid earth, no solar effect, no effect from ocean tides, and a two-dimensional geometry, my calculation in this answer gives the following for $g_Z$, the apparent field when the moon is at the zenith, and $g_N$, when the moon is at its nadir.
$$ \frac{g_N}{g_0} = 1 -\frac{ 2Gmr}{g_0R^3} + \frac{3Gmr^2}{g_0R^4} $$
$$ \frac{g_Z}{g_0} = 1 -\frac{ 2Gmr}{g_0R^3} - \frac{3Gmr^2}{g_0R^4} $$
The difference is $(6Gmr^2/g_0R^4)=6\times10^{-9}$, which is far too small to explain the observed diurnal effect.
I gather that ocean tides can have not just a semidiurnal component but a diurnal one as well. I don't know why this is. Whatever the mechanism is, conceivably that same mechanism would also cause the diurnal effect observed here. I assume that the gravitational field of the ocean is not itself responsible for the effect observed here, since the experiment was done in Boulder, Colorado.
The spectacular agreement between theory and experiment shows that the diurnal experiment must be well understood theoretically. What causes it?
 A: I posted a link to a summary paper on tides in a comment yesterday. That paper is Agnew, D. C. (2007), "Earth Tides", pp. 163-195 in Treatise on Geophysics: Geodesy, T. A. Herring, ed., Elsevier. That paper contains the answer to your question.
I don't know how long that link will last, so I'll summarize some of what Agnew described. This is a summary paper; there's nothing new here. Much of this is 100 years old or older. The key work on this was done by Sir William Thomson, George Darwin (Charles's son), Doodson (google "Doodson number"), and A.E.H. Love (google "Love number", but watch out for the mis-hits.)

Suppose the Earth is some distance $R(t)$ from a gravitating body of mass $M$, measured center of mass to center of mass, and suppose the angle between the line between those two bodies and some point of interest on the surface of the Earth is $\alpha(t)$. The gravitational potential energy due to the gravitating body at that point is $V(t) = \frac{GM}{\rho(t)}$ where $\rho(t)$ is the distance between the point of interest and the gravitating body. (Note: I'm adopting the convention that potential energy is positive, which is fairly standard in treatises on the tides.) Assuming a spherical earth of radius $r$, $\rho(t)$ can be written in terms of $R$ and $\alpha$
$$V(t) = \frac{GM}{R(t)}\frac 1 {\sqrt{1+(r/R)^2-2(r/R)\cos\alpha(t)}}$$
Expanding this using Legendre polynomials yields
$$V(t) = \frac{GM}{R(t)}\sum_{n=0}^{\infty} \left(\frac r R\right)^n P_n(\cos\alpha) $$
We want to omit the $n=0$ and $n=1$ terms. The $n=0$ term can be omitted since it has no gradient (we ultimately want force), and the $n=1$ term is the potential at the center of the Earth. Thus the tide generating potential is
$$V_{\text{tide}}(t) = \frac{GM}{R(t)}\sum_{n=2}^{\infty} \left(\frac r R\right)^n P_n(\cos\alpha) $$
The next step is to re-expand this in terms of spherical harmonics. That angle $\alpha$ is a function of where the gravitating body is in space and time, how the Earth is oriented in time, and the latitude and longitude of the point.
Some spherical cow assumptions: Assume the Earth is rotating uniformly with angular velocity $\Omega$, the point in question is at 0° latitude, 0° longitude, that the body is orbiting circularly with angular velocity $\beta$ and inclination $\varepsilon$ , and that at time $t=0$ the body was at its ascending node with a longitude of ascending node equal to zero.
With a lot of work, the $n=2, m=2$ term of the spherical harmonic expansion leads to three harmonics with angular frequencies of $2\Omega$, $2\Omega-2\beta$, and $2\Omega+2\beta$. These are the semidiurnal tides. The third term is typically negligibly small. With multiple gravitating bodies, all will contribute a term to the twice per sidereal day ($2\Omega$). This is the semidiurnal lunisolar tide, also fairly small. The $2\Omega-2\beta$ term is huge. For the Moon, this is a period of 12.42 hours. For the Sun, it's exactly 12 hours.
With even more work, the $n=2, m=1$ term of the spherical harmonic expansion leads to three more harmonics with angular frequencies of $\Omega$, $\Omega-2\beta$, and $\Omega+2\beta$. The $\Omega$ term once again comprises contributions from multiple bodies. The $\Omega-2\beta$ terms are unique per body. These are the diurnal tides, and they are what you are seeing in that graph.
The picture becomes much more complex when you get rid of those spherical cow assumptions.
A: An overview of how to do the tidal corrections is at http://gravmag.ou.edu/reduce/reduce.html (from Googling 'gravity tide correction'). You might also follow up looking at http://www.applied-gravity.com/gb/html/tides.html.
From http://eclipse.gsfc.nasa.gov/phase/phases1901.html one can see that May 4th of 1981 (the Zumberge paper) was a new moon.  For the first link provided, the timescale is relative to March 25th, 1993, which is two days after the new moon.  The second link shows the tidal variations over a full month (September 2003, 9/25 is the new moon).
Hope that helps...  
