You can talk to the following people to receive your special items on the specific days:

Faida (Dragon Bridge)
AmbarysRendar (New Gnisis Cornerclub)
Elda (Candlehearth Hall)
Hulda (Bannered Mare)
Wilhelm (Vilemyr Inn)
ValgaVinicia (Dead Man's Drink)
Frabbi (Silver-Blood Inn)
Kleppr (Silver-Blood Inn)
TalenJei (Bee and Barb)
Keerava (Bee and Barb)
CorpulusVinius (Winking Skeever)
Jonna (Moorside Inn)
Orgnar (Sleeping Giant)
Hadring (Nightgate Inn)
Thoring (Windpeak Inn)
Mralki (Frostfruit Inn)
Iddra (Braidwood Inn)
Eydis (Old Hroldan Inn)
Dagur (The Frozen Hearth)

If you kill the innkeeper of a particular town, the replacement won't give you any gifts. The innkeeper is the center of every town, so the replacement likely won't be feeling too generous. This will be fixed in future versions.