There is no good reason for Italy to join the war on the CP side. There wasn't a very good reason to join on the Entente side either, they really overestimated how well the Brits would do in forcing the straights.
While the Italians certainly put a little pressure on the side they go against, its pretty easy to defend against Italy no matter who they join. Italy would probably fall pretty fast against the Entente. The best bet for the CP might even be a neutral Italy, at least then they can import through the blockade.
The only possible way Italy could matter is if it somehow affected the way the Marne turned out in 1914. That requires immediate entry and fast mobilization, not sure even then. 1915-1917 are just worthless slogging matches on the western front. If anything a few less Entente troops there might mean a few less dumb offensives.
There are a lot of reasons why Italy could decide to join the Central Powers:
1) If the Germans battlefield success convinced them that the Germans were likely to win, then any offer from the Entente would be worthless
2) The Italians didn't like Austria but they didn't really relish Russia as a neighbor and they also had a lot of problems with France as well
3) Serbian expansionism could threaten Italian domination over the Adriatic as well. Disagreements with Serbian claims was one of the bigger stumbling blocks to Italian entry on behalf of the Entente
4) In a Central Power victory, the Germans would not be so beholden to Austria and they could offer Italy protection against Austria. Indeed, the Germans might come to think that partitioning Austria was in their interests
5) The Entente had a lot of territory that Italy could find quite useful- Algeria, Tunis and Morocco for one
6) Italy could offer the Germans a lot in WWI. Immediate entry would have been best as it could have drawn off five to ten French divisions while suppling troops for the Alsatian front. The Italian fleet could also disrupt French reinforcements from arriving from Algeria
But even later, Italian entrance could do a lot. It would effectively end Franco-British control over the Mediterranean and make that Sea hotly contested. It would likely be a no mans zone where nothing much got through at all for either side. This would effectively end the Gallopoli campaign, isolate Serbia and free up the Austrian forces sent to the Italian front. Russia and Serbia are going down hard in this scenario and Romania and Greece aren't getting involved unless they also join the CPs
These are serious gains for the Central Powers Given the close run thing that WWI is, Italian entrance on behalf of her Triple Alliance partners would definitely tilt the balance enough to give Germany the victory