Are there specific times when morning and evening prayer are supposed to be said?.
There is no specific time, such as Morning Prayer at 7.00 am. But the liturgical books do encourage Morning Prayer to be in the morning, and Evening Prayer to be in the evening.
For example, in the General Introduction to the Liturgy of the Hours: “39. Vespers is celebrated in the evening when the day is drawing to a close, …”.
The 1963 Constitution on the Sacred Liturgy (at
vatican.va/archive/hist_councils/ii_vatican_council/documents/vat-ii_const_19631204_sacrosanctum-concilium_en.html ) includes:
“88. Because the purpose of the office is to sanctify the day, the traditional sequence of the hours is to be restored so that once again they may be genuinely related to the time of the day when they are prayed, as far as this may be possible. Moreover, it will be necessary to take into account the modern conditions in which daily life has to be lived, especially by those who are called to labor in apostolic works.”
Why would this need to be said? I think the practice was to anticipate the prayer. If a priest said Morning Prayer the night before, the he would have satisfied his obligation to say Morning Prayer, and have given himself extra flexibility the next morning.
Public prayer of the Liturgy of the Hours is encouraged in the General Introduction to the Liturgy of the Hours:
“40. In the prayer of the Christian community, Lauds and Vespers are of the highest importance. Their public and common celebration should be encouraged especially among those who lead a common life. The recitation of these prayers is also recommended for the individual faithful who are not able to participate in a common celebration.” (Divine Office, published by E.J. Dwyer, Sydney, 1974, ISBN 085574233X, page xli.)
So public prayer will require a specific time. So in this sense a specific time is encouraged, without a particular time being given.