Coventry is an indoor city in the sense that its main attractions — the cathedral complex, the Transport Museum, the Herbert, the guildhall — are not weather-dependent. You can visit at any time of year and have a full day. That said, Spon Street, Greyfriars Green, and the cathedral ruins are more pleasant when dry, and the courtyard almshouses of Ford's Hospital and Bond's Hospital are best visited in decent light.
Summer brings the most activity, with the university students still around in June and events carried over from the City of Culture legacy programme. The Christmas markets in Broadgate are popular in December and fill the centre more usefully than the rest of winter. Spring and early autumn are the least crowded and the most comfortable for walking. Coventry gets roughly the same weather as Birmingham — mild, frequently overcast, with rain distributed fairly evenly through the year. A warm November day is perfectly viable; a wet July is not unusual.
There is no major annual event worth timing a trip around specifically, though Godiva Festival — a free music festival held in War Memorial Park each summer — draws significant crowds from across the region.