Even though in most of the area of the park dogs are not allowed (which is clearly marked by the signs), there is a short pathway designated for the dog owners – it starts from Koritsas street (on the left of the Municipality Sporting Center of Strovolos) and ends at the parking lot at D.Liperti Street.
You will not be able to enjoy lengthy walks with your dog or let your furry pal loose (there is just too many people at any given time), but the park provides for the other comforts – proper footpath, sitting areas, bins for dog waste, street light etc. The dogs are not allowed to the area were the kiosk and cafe is.
The dog owners however tend to walk their dogs in the neighboring English School area (around their tennis courts and behind the field track, where they even get the dogs loose), even though this is not allowed and stated so in the big sign next to the entrance (to all fairness, someone deleted “no” from the sign in English 
). We don't remember the time when we have been to the place and did not see another dog enjoying the day out.
For us, however, this park is a “no-no”. Not only because Buddy needs a long and tiring walk, but also because the park and the surrounding areas are packed with the athletes playing tennis, football, volleyball etc. and since our dog thinks that all balls in the world belong to him (Labrador owners should know what we are talking about ), we try to avoid it.