Precedence in Government time is given to private Members' bills only very rarely. The last occasion recorded in the Sessional Returns was the Census (Amendment) Bill [Lords] in 1999-2000.
An exhaustive list of private Members' and Peers' bills which were taken up by the Government in the second House is not held centrally and could be compiled only at disproportionate cost.
I am aware of only one example of such a bill—the Forced Marriages (Civil Protection) Bill [Lords], in Session 2006-07.
In addition, the Census (Amendment) Bill [Lords], though it was taken up by a private Member, was given precedence in Government time in Session 1999-2000.