So 'de rigueur' should be grey pin stripe trousers. I assume these would be full rise and with or without braces depending on whether they have pulls on the sides of the trousers. My thinking on the morning coat purchase was that at the BIN price I would not be able to hire one at such a good price so it made sense to own one for those rare occasions rather than a rental that perhaps dozens of other people had already worn previously.
Better to have one and not need it than to need one and not have it ;-)
'Stone me, what a life....' (Tony Hancock)
As I am going to Ascot this year and didn´t want to hire a morning suit (for the obvious reason Tenorclef stated) I have bought my own. Striped trousers are called "Stresemann" trousers in Germany after Gustav Stresemann who was chancellor in 1923. Apart from the trousers the jacket originally was grey, as you wear it before the evening. Later black jackets came up which could be worn with different trousers after six o´clock, although a smoking would be more appropriate.