Is it possible to produce gravitational waves artificially? 
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*Why don't they make a ball with irregularities, say the size of a tennis ball, then spin it very rapidly, so it would produce gravitational waves like a spinning star with irregularities on it? Is that not possible with our current technology? 

*Also since gravitational waves can cause time dilation, wouldn't we be able to make some sort of a time machine with that concept?
 A: Calculating the power emitted as gravitational waves is relatively straightforward, and you'll find it described in any advanced work on GR. I found a nice description in Gravitational Waves: Sources, Detectors and Searches. To summarise an awful lot of algebra, the power emitted as gravitational waves by a rotating object is approximately:
$$ P = \frac{32}{5} \frac{G}{c^5} I_{zz}^2 \epsilon^2 \omega^6 $$
where $\omega$ is the angular equency of the rotation and $I_{zz}^2 \epsilon^2$ is related to the geometry (the quadrupole moment) of the rotating object.
The problem is that factor of $G/c^5$:
$$ \frac{G}{c^5} \approx 3 \times 10^{-53} $$
This is such a tiny number that nothing we could conceivably construct in the lab could produce a detectable quantity of gravitational waves. It takes an object with a huge quadrupole moment, like a neutron star binary, to produce any measurable emission.
A: Gravitational waves are weak. The reason that we try to find them coming from huge astronomy bodies is because we need a lot of mass to produce a measurable gravitational wave.

As you can see, gravity is very weak compared to the other fundamental forces. This is why we need need huge masses to measure them.
You could not make a time machine with a gravitational wave for the same reason that you cannot make a time machine with gravity or by going at close to speed of light.
A: I still believe that black hole merger is the most efficient way.
If we can create micro black hole binaries in laboratory, and let them coalesce, they can emit significant amount of gravitational wave. By tuning the trajectories properly, the amount of energy radiated via gravitational radiation can be up to 9.95% of their rest mass. Don't let them collide face to face which only give off 0.2% of the energy. Although it is very hard to create micro black holes and modulate the radiation, it is still the most practical way in my opinion.
Since general relativity is a nonlinear theory, strong gravitational radiation source is more efficient than weak counterpart.
Citation: On the mass radiated by coalescing black hole binaries
