The problem with the Italian Army in Africa was more than just the tanks.
1. Graziani, who decently understood logistics, did not understand mobile warfare. He did after all not command a mobile force, but rather 100 000 marching men.
2. The infrastructure in Libya was not suited to supply a large amount of men and vehicles.
3. The Italians, who might have had resources enough to fight on one front, tried to invade Greece while they needed to ship everything they had to Libya.
What the Italians need to be more successful in Libya:
1. A commander who understands mobile warfare. Bergonzoli might be such a person. He must also be able to resist Mussolini and have enough influence to make sure that Greece is not attacked, but that all resources go to Libya. These two traits I think Bergonzoli lack, he was not senior enough. Badoglio might do the trick, if he does not die in a plane crash.
2. Badoglio, as governor of Libya, might, just might, undertake infrastructure projects needed. The narrow gauge railroad extended to the Egyptian border instead of just Djebel Abdkhar could help a lot.
3. Absolute priority for the Libyan front. I mean both armoured divisions, all three motorised or semi-motorised divisions, breaking up infantry divisions to provide manual labout, plenty of artillery (the most modern), taking all the motorised small units from corps and armies and putting it there. It means the Italians in Libya might be a force of 70 000 men, fully motorised, with 100 M11/39 tanks, 50 Lancia armoured cars. 100 L3/38 tankettes (with 13,2mm autocannon) and 100 L3/35 tankettes and perhaps 20 L3/35 flame tankettes. They'll have 200 or so 47mm AT guns, ~100 65mm guns for direct fire, ~200 100mm howitzers, ~50 heavy artillery pieces and the support of most of the air force.
It will be a stretch to supply these forces, especially in offensive manouvres, but M13/40 tanks should be rolling in, and if all supplies goes to Libya, it should be possible.