You can get an array of parts touching it. Using :GetTouchingParts()

parts = script.Parent:GetTouchingParts()

You can use the # Operator to see how many of something is in a table, so if it's 0, nothing is touching it.

parts = script.Parent:GetTouchingParts()
if #parts >= 0 then
    print("No parts touching")
end

Now because it's a table we could do special things with it like use a generic for loop.

parts = script.Parent:GetTouchingParts()

for _,part in pairs(parts) do
    print(part.Name.." is touching my parent.")
end

Final Product

local parts

while wait() do --Not the best way to do this
    parts = script.Parent:GetTouchingParts()
end

Hope it helps!

Other Stuff

DragonODeath gave me an idea. I thought about using the Touched event. I thought about it before and realized it isn't very reliable, but I thought of a solution:

parts = {}

function NotOnTable(part)
    for _,p in pairs(parts) do
        if part ~= p then
            return false
        end
    end
    return true
end

script.Parent.Touched:connect(function(p)
    if NotOnTable(p) then
        local pos = #parts+1
        table.insert(parts, p,pos)
        local num = Instance.new("IntValue", p)
        num.Name = "TableThingForScript"
        num.Value = pos
    end
end)

script.Parent.TouchEnded:connect(function(p)
    for _,pa in pairs(parts) do
        if pa == p  and p:FindFirstChild("TableThingForScript") then
            table.remove(parts,p.TableTingForScript.Value)
            p.TableThingForScript:Destroy()
        end
    end
end)