"Founds of an informal organization that's been around for several years want to form an LLC. One of the founders (we'll call Bob) has a friend that own's the domain."
In the beginning, did this friend register the domain name for his own use or at the request of Bob? If registered on behalf of Bob did the friend receive payment to cover the cost? If it was registered on Bob's request for him then it should have been done with him as the registrant and he could ask his friend to update the registrant name and email address with info as he provides. Ideally Bob will have some paperwork that can be used if needed to prove the name was registered on his behalf and not for his friend's own use. Once the registrant email address has been updated, Bob/Joe
"Bob doesn't know how to manage domain registrations, so Bob told his friend it was okay to transfer the domain to one of the other founders responsible for IT (Joe). Their friend is hesitant for whatever reason; instead giving Joe access to the management of the domain."
It's possible here that Bob's friend does not understand that you are trying to take legal and not just technical control of the domain name but thinks you just need to configure something differently. In circumstances like this you may simply need to get Bob to explain clearly what the situation is and that he needs the domain registrant to be changed to Joe who will take responsibility for it going forward. If Bob's friend has any issues with this at least then you'll get to find out what they are. If he doesn't know Joe very well, perhaps he would feel more confident to transfer it to you instead, and then you can let Joe manage it from there.
If Bob's friend has been paying for the domain name himself without having costs reimbursed then it may help to offer at minimum to reimburse his costs to date, or if that is insufficient you need to make an offer to purchase the domain name from him, since technically the domain registrant is the legal owner as far as the domain name registry is concerned.
"Joe doesn't want to push too hard and strain his relationship with Bob or make Bob's friend uncooperative. However he would still like to secure legal ownership of the domain by the business."
In order to ensure continued friendship it is probably best if all three of you meet up together, the situation is explained clearly to Bob in advance, and then to Bob's friend in the meeting, and then just keep it light and ask if any assistance is required, let them know they can contact you with any questions, give Bob's friend opportunity to voice any concerns etc. It may simply be that you need an official purchase agreement and to make a payment of some amount that leaves all parties happy at the end of the meeting - Bob's friend may just feel that he's owed something for his trouble - so have such an agreement prepared with you in a fill-in-the-blanks format so that only one meeting is required.
"What type of contract can Joe have Bob's friend sign, that establishes their business as the owner of the domain name without forcing Bob's friend to immediately transfer it to Joe or the business?"
A purchase agreement is the right contract, however it is important that Bob's friend transfers the domain name to Bob or Joe ASAP. If you are concerned you may end up paying and still not get the domain name ownership, you could place the payment with an escrow service which doesn't release the payment until the domain ownership transfer is completed. If you are prepared to go on trust, then make sure you have sufficient documentation so support your case if you needed to take Bob's friend to court for not transferring the domain name as agreed in the signed purchase agreement.
At the end of the day if Bob's friend is unwilling to transfer legal ownership of the domain name, I would suggest you acquire a different domain name to use for your business, even if this means having to change the business name too. As the legal registrant you can't force him to do anything unless you have sufficient documentation to show he's in breach of some sort of contract and get secure a court order (this will likely cost you more than purchasing it from him, both in finances and friendships).
Whilst I would suggest you don't wait until the business is formed to gain control of the domain name, since having the domain name may be critical to using the name for the business, it is of paramount importance that whoever the domain is transferred to can be trusted to further transfer the domain ownership into the business name once properly formed.