Ethiopia is can be visited at any time of year. People are often advised against travelling during the rainy season, which normally runs from June until early October, but with Lalibela being accessible all through this is less of an issue that it used to be. Indeed, having travelled in Ethiopia at most times of year myself, I actually feel the rain season is my favorite period, partially because there are fewer other tourists at sites such as Lalibela, but above all because the scenery is so much more impressive when the countryside is green and well watered. A lovely time of year is September through to early October, when the whole country is a riot of wild meskel flowers.
The most popular time to visit Ethiopia is between October and January, when the rains are over but the countryside is still quite green. Many travellers try to schedule their trip to coincide with important festivals such as Ethiopian New Year, Ethiopian Christmas, Timket (Epiphany) and others. The European winter is also the best time for birds, as resident species are supplemented by large numbers of Palearctic migrants.
One area where travel options are restricted during the rains is South Omo. The rains here typically fall in April and May, but they may run earlier or later, for which reason March and June are also probably best avoided, as are the short rains in October.
Itineraries are subjective things, dependent on how much time you have, you’re chosen or enforced style of travel, and your interests. The simplistic itineraries included in many travel guides annoy me for several reasons. First, they tend to assume we all have the interests. Secondly, they are packaged into periods that may not suite everyone. Thirdly, they encourage an inflexible approach to travel and discourage initiative and adventurousness. Finally, in countries that I know well, they always seem to be ridiculously crammed-fine on paper but in reality they would involve spending most of your time in the country whizzing about in a or a bus.
If there is a single piece of advice I would give any visitor to Ethiopia (or to any other country for that matter), it is to allocate your time realistically. You can, for instance, easily cover the main attractions of historical circuits by air in nine or ten days. You could, at a push, do it in seven days, but may advice to somebody with only the week in the country would be to drop one of the places off your itinerary. You will enjoy yourself more, and get far more from the places you visit, if you are not constantly operating behind the clock. Much the same can be said for visitors bussing around the historical circuit. If you really wanted to, you could cover the main attractions in two weeks, but anything from eight to ten of those14 days would be dominated by long bus trips. In Africa terms, Ethiopian buses are fine as these things go-but believe me, there is a limit to the number of trips you can handle in rapid succession.