ZAB Controller described a conflict event involving a VFR aircraft descending for PRC and an air carrier departure from PHX; causal factors included weather deviations; dropped Data Block and absent Conflict Alert capabilities.

Narrative

After a busy session with weather deviations on both arrivals and departures into Phoenix airspace; the traffic was getting lighter. I was sending a VFR aircraft at 17;500 northeast bound through Luke (LUF) Approaches airspace to land at Prescott. The RADAR hand off was completed and the Data Block was dropped as soon as it entered LUF airspace. An A320 was a departure out of Phoenix deviated northwards approximately 12 miles north of BXK. At the time I dropped the VFR target; I determined that the A320 and the VFR would not be a factor due to altitude differences. While I was giving a briefing to a relieving controller; the A320 reported an RA that they had to climb faster. One factor may have been that the VFR also deviated north as well as the A320; tying them up further. The big factor is that this confliction occurred in LUF's airspace thus there was no Conflict Alert. Another factor is the winding down from a very busy session and that the CIC acted as a limited D-Side during the busy session and I didn't have a D-side at the time of the incident. Recommendation; I think that I should have had a D-Side at the time or at least during the busy session; in fact; I requested a D-Side. The other problem is the way that the system is set up. The aircraft was leaving Phoenix Approach; transiting LUF Approach and talking to ZAB. In this area; there is not Conflict Alert. This is an issue that has occurred before with Phoenix Approach.