The Tasbeeh/Rosary
The author of Mirqat (A Hadith Commentary) and the author of Raddul Mahtaar (an authoritative work on Hanafi Fiqh) have stated (in exposition of the aforementioned Hadith) that Rasulullah (sallallahu alayhi wasallam) did not prohibit (Hadhrat Safiyya radhiyallahu anha-from using date-stones to count) after noticing this.
Therefore the validity of the popular tasbeeh (rosary) emerges from a Hadith-e-Taqreeri (a Hadith in which Rasulullah-sallallahu alayhi wasallam-corroborates a statement or action of a Sahaabi / Sahaabiya by his silence). The reason for this validity is that there is no significant difference between date-stones (which is mentioned in the Hadith) and the popular tasbeeh besides one being stringed and the other loose. This difference is no cause for prohibition. Thus, the view of one who says it is a bid'at is unacceptable.
The Honourable Mashaa-ikh (Qaddasaallaahu Sirruhum) have called the tasbeeh 'Taaziyanah-eShaitaan' or a 'Whip for Shaitaan'.
Someone saw Hadhrat Junaid Baghdaadi (rahmatullah alayh) with a tasbeeh in his hand and queried:
"What is the need for it (the tasbeeh) when you have ascended to the limits of spiritual progress?"
Hadhrat Junaid (rahmatullah alayh) replied: "How can we abandon something by virtue of which we have reached Allah?"
The Great Saints of Islam have given it the title Muzakkirah or The Reminder, since having it in the hand reminds one to recite something or the other.
THE JOINTS OF THE FINGERS
To count with the joints of the fingers is likewise Masnoon and this is established through a Hadithe-Qowli (saying of Rasulullah-sallallahu alayhi wasallam) and Fe'li (deed of Rasulullah-sallallahu alayhi wasallam).
Tirmithi narrates from Hadhrat Yaseera (radhiyallahu anha) that Rasulullah (sallallahu alayhi wasallam) told women: "Engage in tasebeeb, tahleel and taqdees (i.e. engage in various forms of Zikr) and keep count with the joints of the Fingers. On the Day of Qiyaamah these fingers will be questioned and they will be made to speak."
Abu Dawood narrates from Hadhrat Abdullah Bin Amr Bin al-'Aas (radhiyallahu anhu):
"I Saw Rasulullah (sallallahu alayhi wasallam) used to keep count of tasbeeh by closing the fingers."
Ibn Qudaama, one of the narrators in the chain, explains:
"That is, with his (Rasulullah's-sallallahu alayhi wasallam) right hand,"
However, literally, counting with the finger has a broad meaning. Hence the author of Hirz states: "Whether one opens and closes the fingers, or fingers are pressed, or the thumb is placed along the tips of the fingers."
In other words, in whichever manner one counts with the fingers the actual Sunnat is obtained. Determining any particular method is not stipulated. Despite this, it is understood from the Ahaadith that in the time of Rasulullah (sallallahu alayhi wasallam) the manner of keeping count with the forgers was indeed fixed.
Now the zaakir (one who engages in Zikr) has the option, whether to keep a tasbeeh (rosary) in view of the ease in it, or he may count with the fingers since the virtue is greater. Then again he has the option of counting with the finger in the aforementioned (in the kitaab 'Aqd-e-Anaamil) method or any other method which has reached him via his Mashaa-ikh.
The actual purpose is to ward off negligence as stated towards the end of the Hadith on counting with the fingers. The gist of which is:
"DO NOT BE NEGLECTFUL! OTHERWISE YOU WILL DE DRIVEN AWAY FROM (THE) MERCY (OF ALLAH TA'ALA)."