Before going too complicated see if your receiver has a 300 ohm input for the antenna.
If so, it is easy to fabricate an antenna with simple 300 ohm twinlead lines. It can then be taped to a window or the ceiling.
If your receiver only has a coax input (75 ohm ) a simple balun will change the balanced 300 to unbalanced coax at 75 ohm. They cost only a few dollars.
http://users.wfu.edu/matthews/misc/dipole.htmlIt may not be the best but it is easy to conceal in an unobtrusive spot (if you want, I have not

).
Here is mine in my workshop in the basement. Works very well. Depending on the weather I sometime have to move one arm to a different angle with a thumbtack.
The antenna is about 150cm long but was designed for TV. If I remember correctly FM is located between the old channel 6 and 7 in US Canada if you want to use the table in the link.
At any rate if you are about to change the angle between the two legs for best reception this should work fine.