If it has to be Italian, I think you could do with Barbera if you are looking for a red wine which is not high in tannins.
Non-pretentious wines from Nero d'Avola can also fit your need, for Nero d'Avola is typically interesting, with spicy notes and not big tannins, all in a rounded style. Same with Cerasuolo de Vittoria (typically Nero d'Avola and Frappato). IMHO, wines from Sicily are very versatile to go with many Italian dishes, they are not that expensive (save the top cuvées, which I often like not that much).
You may also want to explore Rioja, specially those made in a more classic style. For example, López de Heredia Viña Cubillo is typically an interesting red with not that much tannin.
If your problem is with histamines, or with added sulphur at the time of bottling, looking for somewhat aged wines can help. Viña Cubillo current release is 2005 so it is usually quite a digestive wine IMHO.
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