I90 Controller experienced a loss of separation between an arrival and departure when both aircraft were in weather deviation maneuvers and response to instructions were slow. Lack of staffing was listed as a causal factor.

Narrative

While working several departing aircraft on the I90 Departure South position; many of them deviating around areas of weather; I had issued a heading of 060 and a climb to 16;000 feet to Aircraft X once it had passed an IAH arrival. At approx XA20Z the FLM came over to me to ensure I saw a deviating arrival; Aircraft Y level at 6;000 and approximately 6 miles southeast of my traffic heading north. I observed Aircraft X to be leaving approximately 5;400 feet; so I believe I issued a turn to 360 degrees and immediate descent to 5;000 feet. These may not have been in the same transmission. The pilot of Aircraft X acknowledged. I looked at other traffic; then right back to Aircraft X; and saw that he was still in a climb out of approximately 6;500; so I told him to continue climb; and expedite out of 7;000. Again the pilot acknowledged. At this point the aircraft seemed to be about 3 miles from each other and the Aircraft Y jet was turning westerly. Aircraft X then started descending again instead of climbing and so I had him expedite to 5000. Recommendation; ensure adequate staffing exists to provide either a position coordinator or controller to open the East departure sector during periods of bad weather. This is usually done here but there were not enough controllers available at the time.