Could an object from outer space with the right velocity and orbit come into contact with the surface of our planet in a "slowish" manner?
Yes, spacecraft do it all the time by using air resistance (and sometimes rockets) to slow down.
Meteorites enter the atmosphere at high speed, typically 10-70 km/sec, but the smaller ones are slowed by air resistance, so they typically hit the surface at just a few hundred kilometers per hour. Reference: http://csep10.phys.utk.edu/astr161/lect/meteors/impacts.html (that link is now dead).
As gerrit points out in comments, a sufficiently small micrometeroid, like a dust particle, probably could hit the surface gently.
Larger bodies are not affected nearly as much by the atmosphere. For any such body, the velocity at impact is going to be at least several kilometers per second. A body moving obliquely in the same direction as the Earth's rotation would have a slightly lower speed at impact, but the impact still could not be described as "gentle"; the Earth's rotational speed is still a small fraction of orbital or escape velocity.
Here's one way to think of it. Freefall trajectories are reversible. If you watch a movie of an incoming body in reverse, it still makes physical sense (ignoring air resistance). Any meteorite hitting the surface has to have been in deep space at some point before the impact. If there were a trajectory that allowed such a body to have a "gentle" impact speed, then it would be possible to start with the same body near the surface at the same "gentle" speed, but in the opposite direction, and have it reach deep space. Unless the meteorite has its own propulsion system, that's just not going to happen.
You can get to space with a lower starting speed by moving along with the Earth's rotation - which is why most rockets are launched to the east, to take advantage of that. Reversing such a trajectory can result in a slightly slower impact, but only slightly.
It is difficult to see how. Most comets and asteroids would encounter the Earth on a crossing orbit and the encounter velocity would be roughly the vector sum of the Earth's velocity around the Sun (of order 30 km/s) and the individual velocity of the rogue object.
Even if you were to arrange it so that the asteroid/comet was diverted by something else so that it "caught up" with the Earth from behind travelling at an initially low relative velocity, there is the additional influence of the Earth's own gravitational potential. This would accelerate the approaching object to something like the order of the escape velocity from the Earth's surface - about 11 km/s.
This fairly authoritative site on calculating the effect of asteroid/comet impacts suggests a minimum impact velocity of 11 km/s, which is indeed the Earth's escape velocity.
Edit: (And credit to Keith Thompson for pointing it out). These are the speeds at the top of the atmosphere. If the objects are smaller than 20-30m, then the atmosphere will basically take out most of that kinetic energy, so for small objects, a relatively slow impact is de riguer. But for anything larger than $\sim$50 m, it is basically the full 11 km/s or more. http://www.lsst.org/lsst/science/scientist_near_earth_objects_neoquant
“Trajectories are reversible” gives a good clue as to the conditions for a low speed impact. Consider two planets in a close, fast orbit such that objects on the far surface of a planet, directly opposite the other planet, are virtually weightless. At this location acceleration due to gravity of the system is just slightly greater than the tendency to be ‘flung’ away (centripetal acceleration). Under these conditions a rock could be propelled upwards relatively slowly and move away from the planets. Just reverse everything and a rock could land slowly. I admit this is contrived, the atmosphere is likely to be lost, plus I hope Earth won’t be in this situation any time soon!