May one rent out a funeral room out to goyim that will have church services in it during that time?
Yes, one can be lenient for this.
The question of renting a house for purposes of Church services is debated by authorities, and depends on the classification of Christianity as idolatry.
However, in this case the rental is not for the purpose of a Church, but for a funeral service, and therefore this is possibly similar to the case of renting for living, where idolatry will be brought into the house. This is the subject of a dispute between the Shulchan Aruch and the Shach (Yoreh De’ah 151:10, Shach 17).
For today, the great majority of Protestant denominations of Christianity will not be considered idolatry, and where the rental is for a funeral service and not for an actual Church, one can be lenient.
See also Iggros Moshe (Orach Chaim 3:28 and 1:50) concerning the sale of property as a Church; based on the Shach this will provide additional room for leniency.