The Paleo diet suggests that it is best to avoid dairy foods as many people are intolerant to the lactose in dairy products. Although this may be true, dairy products are important, as they provide calcium for healthy bones.
Both my parents grew up on dairy farms in Victoria and funnily enough, neither of them like milk. They passed on their dislike of plain milk to me and my siblings. So I know how hard it is to get enough calcium without cow’s milk. Considering that dairy products provide our bodies with calcium superior to other sources, it is lucky for me that I like cheese and yoghurt. In fact, a study found those that are allergic to cow's milk as children, were found to have lower bone mineral density as young adults even when they were attempting to consume enough calcium from other foods . The children that couldn’t consume dairy products found it difficult to consume enough calcium from other sources such as nuts, and vegetables to meet their needs.
You may have heard of A2 milk. This may be a good option for those that react to milk in a bad way. A2 milk is from cows that produce a protein known as A2 versus the A1 protein, and is thought to be the protein most cows originally produced. Studies are being undertaken to determine if the A2 protein is better for human consumption, particularly for those that appear to react to normal cows milk. Although this is yet to be confirmed, it is worth trying if you find you don't tolerate milk very well.
Then there is the lactose free products. If you are lactose intolerant, these products will still provide you with the much needed calcium in the same quantities as other milk products.
To help you know if you are having enough dairy to get your calcium needs a serve of dairy is: 
1 cup (250ml) fresh milk, UHT long life, reconstituted powdered milk or buttermilk
½ cup (120ml) evaporated milk
2 slices (40g) or 4 x 3 x 2cm cube (40g) of hard cheese, such as cheddar
½ cup (120g) ricotta cheese
¾ cup (200g) yoghurt
1 cup (250ml) soy, rice or other cereal drink with at least 100mg of added calcium per 100ml
(Also see the bottom of the page for the recommended calcium requirements per day)
If you are still not keen on the idea of having cow’s milk, making sure that you are consuming plenty of food rich in calcium is very important. If you choose a non-dairy milk product, it is a good idea to look for one that has had calcium added to it (ideally 100mg of calcium for every 100ml of milk).
Other foods that have calcium are:
100g almonds with skin
60g sardines, canned in water
½ cup (100g) canned pink salmon with bones
100g firm tofu (check the label as calcium levels vary)  .
leafy green vegetables – broccoli, collards (cabbage family), bok choy, Chinese cabbage and spinach. One cup of cooked spinach contains 100 mg, although only 5% of this may be absorbed. This is due to the high concentration of oxalate, a compound in spinach that reduces calcium absorption. By contrast, 2 cups of cooked broccoli contains about 90 mg of calcium, but the absorption from broccoli is much higher at around 50–60% .
Having these quantities are equivalent to the amount of calcium in a serve of dairy foods. Most people need 2-3 serves a day, but more if you are female and over 51.
Things that interrupt absorption of calcium are:
Low vitamin D levels
Excessive caffeine and alcohol
Diets high in phytates (eg: some cereals and brans) or oxalates (eg: spinach, rhubarb)
Certain medical conditions (eg: coeliac disease, kidney disease) and certain medicines (eg: prednisone, prednisolone)
To improve absorption of calcium we need to be mindful of keeping our vitamin D levels up. Vitamin D is important as it helps our bodies to absorb calcium from our diets. So if you are low in Vitamin D, you will likely not be absorbing enough calcium. The best way to get enough Vitamin D is from the sun. Oily fish also contain Vitamin D, but not normally in high quantities.
Summer Sun Exposure 
Winter Sun Exposure 
As you can see, our dietary choices play a large role in keeping our body healthy. Making sure you are getting enough calcium is very important for your bone health, and dairy is the best way to do that. If you still want to avoid dairy products, you will need to be very mindful of your other food choices.
The Paleo diet has some good points, some bad points and some concerning issues. It is very important to not remove food groups from our diets unless medically advised. If you do choose to go down the Paleo road, you will need to be very diligent in ensuring you are still taking in enough nutrients from all the food groups.
As I have found out the hard way, going on restrictive diets like this are not easy to maintain. I found that when I diverted from the diet, I felt guilty and felt like I had failed. There are other ways to have good health and not get into the rut of dieting then failing and trying again.
A dietitian can help you with this.
Recommended Calcium Intake 
 Nachshon, L., Goldberg, M., Schwartz, N., Sinai, T., Amitzur-Levy, R., Elizur, A., . . . Katz, Y. (2014). Decreased bone mineral density in young adult IgE-mediated cow's milk-allergic patients. Journal of Allergy and Clinical Immunology, 134(5), 1108-1108. doi:10.1016/j.jaci.2014.06.026
 Eat for Health. (2015, July 27). Milk, yoghurt, cheese and/or their alternatives ( mostly reduced fat). Retrieved October 22, 2016, from Eat for Health: https://www.eatforhealth.gov.au/food-essentials/five-food-groups/milk-yoghurt-cheese-andor-their-alternatives-mostly-reduced-fat
 Victoria State Government. (2013, April). Calcium. Retrieved October 22, 2016, from Better Health Channel: https://www.betterhealth.vic.gov.au/health/healthyliving/calcium
 Osteoporosis Australia Medical & Scientific Advisory Committee. (2015, September 3). Calcium. Retrieved October 22, 2016, from Osteoporosis Australia: http://www.osteoporosis.org.au/calcium
 Osteoporosis Australia Medical & Scientific Advisory Committee. (2015, September 3).. . (2016 ). Vitamin D. Retrieved October 2016, 2016, from Osteoporosis Australia: http://www.osteoporosis.org.au/vitamin-d