Pain does have bodies in reserve in the event he needs them. During Pain's assault on Konoha, Inoichi used his clan's justu to go through the mind of Yūdachi. Yūdachi is a genin from the village in which Pain lives, whom was captured and sent to Konoha by Jiraiya.
While traversing through Yūdachi's mind, Inoichi came across a memory in which Yūdachi and another genin were transporting bodies to Pain's tower.
He probed Yūdachi's mind, rapidly going through his memories before arriving at the revelation that Pain had requested of Yūdachi: dead bodies
The body that is seen within this memory ends up being the replacement of Animal Path that was defeated by Jiraiya. Given how it was Jiraiya who sent Yūdachi to Konoha, this memory is long before the defeat of the original Animal Path. This is why Pain was able to recover from the loss of the Animal Path so quickly.
Now... as to having backups with the black receivers. It is possible these said backup bodies have the black receivers already in them, but as they are never show otherwise, we may never know. However, there are a few likely reasons to why Pain did not attempt to summon his backup bodies during his battle with Naruto
Animal path defeated (again)
The Animal Path is shown summoning the other five paths early in the Pain Assault arc. So Pain was very well capable of calling in backups. However, Naruto defeated the Animal Path fairly early in the fight. Due to this path being defeated, Pain lost his way of summoning.
Focusing his chakra
The black receivers in the paths allow Pain to transmit his chakra over long distances in order to control the six paths. When Pain completely destroyed Konoha, he severed the connections to other paths to focus his all of chakra into performing the justu.
Some of the Six Paths Techniques are very chakra-taxing, and in order to use them Nagato must either bring the respective body closer to his position or alternatively cut off control of the other five Paths and focus all of his chakra into the one.
Also, one of the weaknesses of the six paths is that each path has a single ability. Prior knowledge, such as facing them battle, gives you an upper hand in taking them down.
The greatest weakness of his Six Paths of Pain is that each body has only one primary ability; if an enemy has prior knowledge of what body does what, they stand a better chance of defeating the Paths
Pain saw how strong Naruto was, and therefore needed to play his cards right. As Naruto took out the paths one-by-one, rather than calling in backup, Pain distributed the chakra he regained from defeated paths to strengthen the remaining paths.