From a strictly utilitarian perspective, children won't be necessary, in fact, once immortal representations of ourselves inhabit computers; on the other hand, people will not let go of the pleasure and responsibility of bringing up a family any more than they will let go of the pleasures and pains of having a body, even if they choose to use it only very occasionally. It is likely therefore that children will continue to be born even when there will no longer be a need for them in population replacement or evolutionary terms, through a combination of market forces, willingness to conform to ethical breeding guidelines, and availability of space and resources.
There will be plenty of space for there to be more people, in fact, even if the population has not stabilized: many people may choose to let go of their human bodies in favour of RCR and RCC experiences, with occasional physical embodiment in robotic form (the word is wrong, because the bio-electronic construct being temporarily 'inhabited' by the individual may take many physical and psychic forms). Alternatively there may be rationing of physicality by regulation and/or by the market. Of course it will be a human right to enjoy physicality for a certain minimum amount of time, paid for by taxation (unlike death, taxes will indeed always be with us). And presumably by 2100 the human race will be well on the way to creating its extra lebensraum in space. Adventurous spirits will travel to the stars in electronic form and recreate themselves on arrival from local materials.
Outright experimentation in child-bearing will perhaps not be permitted, and the human genome, having been 'cleaned-up' in order to get rid of disease genes and certain anti-social tendencies, will be maintained as a kind of template onto which parents will be permitted to map characteristics from a list of fairly narrowly defined acceptable variations. Musical parents would perhaps want to give their child capacious lungs (the better to sing) or wide hands (the better to play octaves or even tenths). That far seems acceptable: these are improvements, even if not used by the child in later life. If a child of two tennis-playing parents turns out to be musical (and not wanting to use the powerful shoulders it was given), then of course it can be a concert pianist through an RCR surrogate.
What to do though with ever-greater numbers of individuals who are going to live for ever, even if they are stored in chips and don't take up a measurable amount of space or resources? Some of them will no doubt become couch chips. Will people want to switch themselves off out of ennui? There is a growing movement for euthanasia in the early 21st century, but presumably candidates for it are people who are facing imminent and painful death – will there still be candidates for death if it is no longer inevitable? Will there then be rules to isolate people, temporarily or permanently, if they don't contribute to society in a way that is found acceptable by their peers?