Gemara

(Rav): If a bed was designated for coins, one may not move it [on Shabbos].

Objection (Rav Nachman bar Yitzchak - Mishnah): One may move a new Ner, but not a used Ner.

A Ner is made for lighting, yet one may move it before lighting in it. A bed is not made for coins, all the more so it is permitted before it was used for coins!

Correction: Rather, if a bed was designated for coins and one put coins on it, one may not move it. If he did not put coins on it, one may move it.

If it was not designated for coins, if there are coins on it, one may not move it. If not, one may move it, as long as there were not coins on it [all of] Bein ha'Shemashos.

123a (Rav Chinena): All agree about dying (alternatively - weaving) tools. Since people care about them, they fix a place for them. (Therefore, they may not be used for other purposes.)

128a: Rav forbids eating Muktzeh like R. Yehudah, but he permits moving it like R. Shimon.

142b (Mishnah): If coins are on a pillow, he shakes the pillow and they fall off.

(Rav): This is only if he forgot. If he intentionally left it, it is a Bosis for Isur.

Rishonim

Rif and Rosh (21a and 3:20): One may move a bed only if there are no coins on it, whether or not it was designated for coins, as long as there were not coins on it Bein ha'Shemashos. If there were coins on it Bein ha'Shemashos, since it was Muktzeh Bein ha'Shemashos, it is Muktzeh all of Shabbos. It is Muktzah due to Isur. Therefore, one may not move it.

Ran (DH v'Mitah): Rav Yehudah forbids a bed designated for coins, for he holds like R. Yehudah, who forbids Muktzeh. We hold like R. Shimon [who permits Muktzeh], except for Muktzah due to Isur. Therefore, the Rif says that even if he designated it for coins, and put coins on it during the week, it is permitted, as long as they were not on it all of Bein ha'Shemashos. If they were on it all of Bein ha'Shemashos, it is forbidden. This is only if he left them on intentionally. If not, even if they were on it all of Bein ha'Shemashos it is permitted, for it was not Muktzeh Bein ha'Shemashos. We say that if one forgot coins on a pillow, if he needs the pillow, he shakes off the Muktzeh. Similarly, if he needs the place, he moves it with the Muktzeh on it. The Bosis becomes forbidden only if he intentionally left on it.

Rambam (Hilchos Shabbos 25:10): One may not move any Kli she'Melachto l'Isur, e.g. a lamp that was burning on Shabbos, and the Menorah on which the lamp rested, and coins that were on a table. Even if the lamp extinguished or the coins fell off the table, it is forbidden to move it. Any Kli that it was forbidden to move it Bein ha'Shemashos, it is forbidden to move it all of Shabbos, even if the matter that caused the Isur went away.

Rosh (3:20): The Rif did not bring Rav's law, because he holds like R. Yehudah, and we hold like R. Shimon. R. Tam says that R. Shimon agrees about a bed designated for coins if he put coins on it, for one is particular about it and designates a place for it. This is like we say about dying (or weaving) tools, since people care about them, they fix a place for them. He says so because below we say that Rav holds like R. Shimon regarding moving Muktzeh. Therefore, we must say that R. Shimon agrees regarding a bed.

Tosfos (44b DH Yesh): The Gemara must discuss one who put [the Muktzeh on] intentionally. If he forgot, he may shake it off. We discuss one who put it on on Shabbos, If he put it on before Shabbos and it was on Bein ha'Shemashos, it is forbidden even after the Muktzeh is removed. How can one put on intentionally on Shabbos?! We can say that a Nochri or child put on to please an [adult] Yisrael. If so, why didn't Beitzah 26a learn from here that there is no Muktzeh for part of Shabbos? It is because we could say that the Muktzeh was put on to please a Yisrael, with intent to remove it after a while. This is like something that will be finished (become usable) through man [which is permitted]. There is no question based on what I said above that 'Muktzeh for part of Shabbos' applies to eating, but not to moving.

Poskim

Shulchan Aruch (OC 310:7): If there are coins on a bed, or even if there are not now, but there were coins on it Bein ha'Shemashos, one may not move it. Since it was Muktzeh Bein ha'Shemashos, it is Muktzeh for all of Shabbos.

Beis Yosef (DH Hilkach): Rashi explains that if coins were on it even during the week, it was Huktzeh for Isur, and it is forbidden to move it even if the coins were removed during the day. This is unlike a metal lamp, which R. Yehudah permits. That is when it was not designated.

Magen Avraham (4): The Shulchan Aruch connotes that this is even if they were not on it Bein ha'Shemashos, e.g. a Nochri or child put it on it on Shabbos, at the will of a Yisrael, like Tosfos.

Bi'ur Halachah (DH Mitah): This connotes that even if the coins were not on the bed all of Bein ha'Shemashos, it is forbidden to move it when they are on it. The case is, a Nochri or child put on to please an [adult] Yisrael. The Magen Avraham (308:50) brought opinions about whether or not one may shake the coins off. The Magen Avraham (265:2, brought below) leans to say that it did not become a Bosis, since the Muktzeh was not on it Bein ha'Shemashos, so one may shake them off.

Shulchan Aruch (ibid.): The same applies to any Heter on which Isur rests. If there is are not coins on it now, and there were not Bein ha'Shemashos, one may move it even if he designated it for coins and put coins on it before Shabbos, since they were removed before Bein ha'Shemashos.

Gra (DH Aval): Regarding this, the Halachah does not follow Rav, for he holds like R. Yehudah. Regarding the Reisha (Muktzah Machmas Isur), the Halachah follows R. Yehudah, like it says on 157a.

Bi'ur Halachah (DH v'Hanicham): The Shulchan Aruch could have taught a bigger Chidush, that even if he put the coins on on Shabbos and later removed them, since they were not on Bein ha'Shemashos, even if it was special for coins, it is permitted. Rather, the Shulchan Aruch discusses this case to teach unlike R. Tam, who forbids. He discusses when the coins were put on during the day and later removed. He forbids, since it is designated for coins.

Rema: Some forbid if it was designated for coins this and put [Muktzeh] on it, even if it was removed during the day. Therefore, one may not move a money bag, even if the money was removed during the day, unless he did an act, e.g. he opened it below and removed the designation. This is the custom. However, l'Tzorech Gufo or Mekomo is permitted.

Gra (DH Ela): if he did an act, this nullifies his intent of designation, and also the act (of putting coins in it), like it says in Kelim (25:9).

Shulchan Aruch (265:32): On Shabbos, one may not put a Kli under a lamp to catch oil that drips, for this forbids (moving) the Kli.

Magen Avraham (2): However, one may put a Kli under a wax candle. This does not forbid moving the Kli, since he could shake it off [without a loss, so he is wont to do so]. The Beis Yosef says that this is like the latter opinion in 309:4. The first opinion forbids shaking it off, for it is a Bosis for Isur. This is difficult, for all agree that a Bosis for Isur is only if the Isur was on it Bein ha'Shemashos! Hagahos Ashri says that if the Kli holds Heter that one cannot shake off, one may put it under a lamp to catch dripping oil, for one may move it due to the Heter.

Shulchan Aruch (308:27): If peels of food [that was eaten on Shabbos] are not proper for animals to eat, one may not move them. Rather, one shakes the tabletop, and they fall.

Magen Avraham (50): Why is this permitted? The tabletop is a Bosis for Isur! I answer that he did not intend to leave them there the entire day. Alternatively, since there was food there, it is a Bosis for Isur and Heter. Also, he did not put [the peels] there intentionally. He is not concerned where they fall. Tosfos (44b DH Yesh) says so. Even if one puts on on Shabbos, one may not shake it. Based on what I wrote in 266:14, it is not a Bosis unless the Muktzeh was on it Bein ha'Shemashos. Even Tosfos agrees that if the Muktzeh was later removed, it is not a Bosis, since it was not on it Bein ha'Shemashos. The Gemara explicitly says so.